FR2932591A1 - METHOD FOR GENERATING A MODIFYING MODEL OF A FLEXIBLE NAVIGATION DEVICE, MODEL, METHOD AND DEVICE FOR MANAGING THE NAVIGATION OF A MODEL, COMPUTER PROGRAM PRODUCT, AND STORAGE MEDIUM - Google Patents

Abstract

The invention relates to a method for generating an editable model of a flexible navigation device comprising at least one tool. The model can navigate within a virtual structure described by a surface mesh. The method comprises a step of obtaining a plurality of bodies by discretization of the device, each body comprising a hinge for linking said body to another body. According to the invention, the method comprises, for each body, a step of association with the body of a modifiable layer representative of a set of parameters relating to at least one tool of the device.

Description

A method of generating an editable model of a flexible navigation device, model, method and device for managing the navigation of a model, computer program product and storage means. FIELD OF THE DISCLOSURE The field of the invention is that of virtual reality, and in particular the modeling of flexible navigation devices, such as, for example, instruments for exploring tubular or cavity anatomical structures. The invention more specifically relates to the navigation of such models in a virtual environment.

The invention applies in particular, but not exclusively, in virtual reality systems in the context of diagnostic and therapeutic procedures in the field of endovascular surgery, radiology and interventional cardiology, pneumology, urology or the gastroenterology. 2. Background Art The disadvantages of the prior art are discussed below through the particular case of a simulation of endovascular catheterization. It is now possible to apply minimally invasive treatments, using different principles of interaction with tissues using instruments and / or pharmacological agents introduced by intracorporeal routes. These practices add new requirements in terms of learning, planning, gesture and ergonomics. The dexterity of the practitioner has reached its limit and is no longer sufficient to meet the criteria of safety, reliability and traceability of the gesture imposed by the regulatory context. Thus, modern interventional practices require, or even require, for their development a high-tech support, such as for example virtual reality. In the context of diagnostic and therapeutic procedures involving the navigation of flexible instruments within anatomical structures, the implementation of a virtual environment dedicated to the planning of the control gestures of these instruments must make it possible to optimize the preoperative choice. material and to anticipate the difficulties of access to the injury. The specificities and constraints required by endovascular catheterization prompted some teams to propose simulation methods exclusively dedicated to this type of procedure. Generally, these simulations are integrated into specific hardware devices with haptic feedback such as, for example, those marketed by the company Immersion. Numerous techniques for modeling instruments and vascular structures are already known. Among the various types of known techniques, a first technique consists of modeling the structure with cylindrical segments (called bodies). This first modeling technique, called multibody modeling, is notably described in [Dawson, 00] and [Konings, 03] (for the sake of readability, the various documents cited are grouped together in Appendix 1, at the end of the present description) . A second known technique is based on the finite element method. This second modeling technique is notably described in [Lenoir, 06] and [Cotin, 05]. A third technique is to combine the first and second aforementioned known techniques. This third modeling technique is notably described in [Lawton, 99], [Anderson, 02] and [Bhat, 05]. These known techniques have a number of disadvantages. Indeed, these techniques find their limits in the compromise they impose between accuracy of the representation of anatomical structures and computation time. Thus, the inventors have found that in certain situations the integration of patient-specific data, for which the lesions require a precise graphical representation, is not ensured. By accurate graphical representation is meant a representation having a large number of polygons. For example, the graphical representation of a vascular structure and its lesion can be qualified as precise when the surface mesh is reconstructed according to the same sampling as the imagery data acquired. Another major disadvantage of these known techniques lies in the lack of joint simulation of the catheterization instruments. Indeed, current techniques do not simulate simultaneously and dynamically several instruments interacting with anatomical structures and having different mechanical properties. Finally, it should also be noted that these known techniques present a limitation in the realism of the instrument models where the heterogeneity of the mechanical characteristics is not integrated. 3. Objectives of the invention The invention, in at least one of its embodiments, has the particular objective of overcoming these disadvantages of the prior art. More specifically, an objective of the invention, in at least one of its embodiments, is to provide a technique that makes it possible to obtain a realistic modeling of the instruments. Another object of the invention, in at least one of its embodiments, is to provide such a technique which is inexpensive in computation time making it possible to achieve a real-time simulation. Another object of the invention, in at least one of its embodiments, is to provide such a technique which improves the representation accuracy of the structures. Another object of the invention, in at least one of its embodiments, is to provide such a technique which allows a joint navigation of several instruments. Another objective of the invention, in at least one of its embodiments, is to provide such a technique that allows better intervention planning. Another object of the invention, in at least one of its embodiments, is to provide such a technique which is compatible with existing computer hardware. The invention, in at least one of its embodiments, still aims to provide such a technique that is simple to implement and this for a low cost. 4. DISCLOSURE OF THE INVENTION In a particular embodiment of the invention, there is provided a method of generating an editable model of a flexible navigation device comprising at least one tool, said model being able to navigate within a virtual structure described by a surface mesh, said method comprising a step of obtaining a plurality of bodies by discretization of said device, each body comprising a hinge for linking said body to another body.

According to the invention, the generation method comprises, for each body, a step of association with said body of a modifiable layer representative of a set of parameters relating to at least one tool of said device. The invention therefore proposes an original model comprising a plurality of bodies each associated with a parameter layer. This layer is modifiable in that the values of the parameters of this layer change as a function of the evolution of the model within the virtual structure. The invention covers a first case in which the model comprises a single layer. The invention also covers a second case in which the model comprises several distinct layers. By flexible navigation device is meant any flexible instrument that can move within a tubular or cavitary structure. Note that the model can represent a plurality of tools that can slide on each other and can be dependent on each other.

Advantageously, said set of parameters comprises at least one parameter belonging to the group comprising: mechanical parameters of at least one given tool; - shape parameters of at least one given tool; - Visualization parameters of at least one given tool.

Preferably, each body is a rigid cylinder. Advantageously, the method comprises, for each articulation, a step of association with said articulation of at least one determined angular constraint. In another embodiment, the invention relates to an editable model of a flexible navigation device comprising at least one tool, said model being able to navigate within a virtual structure described by a surface mesh, said model comprising a plurality of body, each body including a hinge for binding said body to another body. According to the invention, each body is associated with a modifiable layer representative of a set of parameters relating to at least one tool of said device. In another embodiment, the invention relates to a storage means containing the aforementioned modifiable model. In another embodiment, the invention relates to a computer program product downloadable from a communication network and / or recorded on a computer readable medium and / or executable by a processor, said computer program product comprising instructions program code for implementing the method of generating a modifiable model above, when said program is run on a computer. In another embodiment, the invention relates to a method of managing the navigation of an editable model of a flexible navigation device comprising at least one tool, said model being able to navigate within a virtual structure described by a surface mesh, said model comprising a plurality of bodies, each body being identified by an index number, each body comprising a hinge for binding said body to another body.

According to the invention, the management method comprises the following steps: obtaining a modifiable model, called an initial model, comprising a plurality of bodies each associated with a modifiable layer representative of a set of parameters relating to at least one tool said device; - obtaining a navigation command; - Generation of a modified model, by modifying said initial model according to a modification operation selected from a plurality of modification operations according to said navigation command.

Advantageously, said plurality of modification operations comprises an operation belonging to the group comprising: an operation of modifying a body of said initial model by modifying the modifiable layer associated with said body; an operation of inserting a new body into said initial model; an operation of deleting a body of said initia model; a rotation operation (torque) of said initial model about its axis. Advantageously, the management method comprises, for each articulation, a step of association with said articulation of at least one determined angular constraint.

Advantageously, the management method comprises a step of detecting in said modified model at least one body colliding with said virtual structure and / or with another body. For each colliding body, an angular stress propagation phase is performed. According to an advantageous aspect of the invention, said angular stress propagation phase comprises the following steps: determining a first collision cancellation angle; applying said first collision cancellation angle to the articulation of said colliding body, said body being treated; checking that the articulation of said treated body satisfies said at least one angular constraint associated therewith; in the case of negative verification: applying a second angle to the articulation of said treated body, said second angle allowing the articulation of said treated body to reach said at least one angular constraint; o determining a body to be treated, linked to said treated body and having an index number lower than that of said treated body; o determining a third angle from said second angle and said first collision cancellation angle; o application of said third angle on the articulation of said body to be treated, said body to be treated becoming the treated body before returning to the verification step. Advantageously, the management method comprises a relaxation phase comprising the following steps: determining a fourth relaxation angle; for each treated body, application of said fourth relaxation angle to the articulation of said treated body. Advantageously, the management method comprises a step of detecting at least one blocking of one or more tools in said virtual structure.

In another embodiment, the invention relates to a storage means containing the aforementioned management method. In another embodiment, the invention relates to a computer program product downloadable from a communication network and / or recorded on a computer readable medium and / or executable by a processor, said computer program product comprising instructions program code for implementing the above management method, when said program is executed on a computer. In another embodiment, the invention relates to a device for managing the navigation of an editable model of a flexible navigation device comprising at least one tool, said model being able to navigate within a virtual structure described by a surface mesh, said pattern comprising a plurality of bodies, each body being identified by an index number, each body including a hinge for binding said body to another body. According to the invention, the management device comprises: means for obtaining an modifiable model, called an initial model, comprising a plurality of bodies each associated with an modifiable layer representative of a set of parameters relating to at least one tool of said flexible navigation device; means for obtaining a navigation command; means for generating a modified model making it possible to modify said initial model according to a modification operation chosen from among a plurality of modification operations according to said navigation command. 5. List of Figures Other features and advantages of the invention will appear more clearly on reading the following description of a preferred embodiment, given as a simple illustrative and nonlimiting example, and the accompanying drawings, among which: - Figure 1 shows the geometric structure of a multilayer multi-body model (MBML) according to a particular embodiment of the invention; FIG. 2 shows a connection diagram between the bodies of the MBML model of FIG. 1; FIGS. 3a to 3f illustrate examples of the end shape of tubular tools; FIGS. 4a and 4b illustrate examples of maximum curvature of the geometric structure of the MBML model; FIG. 5 is a simplified diagram of a restoration spring according to a particular embodiment of the invention; FIG. 6 illustrates single-tool and multi-tool layers according to a particular embodiment of the invention; FIG. 7 shows a decomposition of the MBML model according to a particular embodiment of the invention; FIG. 8 presents a flow chart of a particular embodiment of the MBML navigation management method; FIG. 9 presents a flowchart of a particular embodiment of a deformation loop; FIG. 10 schematically illustrates an orthographic virtual camera associated with a body of the MBML model; Figure 11 schematically illustrates a collision between bodies of the MBML model; - Figure 12 schematically illustrates the simulation of the thrust of a tool; FIG. 13 schematically illustrates the evolution of the stiffness parameters during a translation manipulation of a tool; FIGS. 14a and 14b respectively illustrate the addition and deletion of a body during a translation; FIG. 15 schematically illustrates a layer switching during a translation; FIGS. 16a to 16d show examples of simulation and navigation of flexible instruments within tubular structures. 6. Detailed Description 6.1 General Principle The multi-body formalism is used to discretize a flexible navigation device (hereinafter also referred to as an instrument), comprising one or more endovascular tools (eg a guide and a probe), according to a structure. geometrically divided into several bodies interconnected by joints. The general principle of the invention is based on obtaining a model, hereinafter referred to as multi-layer multi-body model (or MBML model, for Multi-Body Multy-Layers), in which each body is associated with a layer of parameters. According to the invention, within a layer are grouped parameters relating to one or more tools and associated with a body. The simulation of the deformable character of the instrument is based on the introduction of constraints at the joints of the geometric structure. The simulation of the dynamic behavior of the tool is thus based on an angular stress propagation coupled to an elastic relaxation. Thus, and as will be seen later, in the particular case where the flexible navigation device comprises two tools (for example a guide and a probe) intended to evolve together within an anatomical structure, three distinct layers are defined. . More precisely, two of them, called single-tool layers, are used for the independent representation of each of the tools (in other words, one defines a single-tool layer for the guide and another single-tool layer for the probe), and the third layer, called the multi-tool layer, is used for the combined representation of the two tools (in other words, a multi-tool layer is defined for the guide plus probe combination). According to the invention, the joint evolution of the tools is simulated by consecutively associating each body with a particular layer. The parameters of each body are then used to calculate the dynamic behavior of the model defined on the geometric structure. 6.2 Geometric Structure of a Multilayer Multilayer Model (MBML) The geometrical structure of an MBML model 100 according to a particular embodiment of the invention is now described with reference to FIG. The geometric structure of the MBML 100 model is decomposed according to a multi-body formalism by a set of non-deformable bodies, numbered from 1 to 4. The topology of the structure is equivalent to a kinematic chain of cylindrical segments connected to each other by spherical links. (For example, ball joints), numbered from 10 to 40. As illustrated, the hinge 10 belongs to the body 1, the hinge 20 to the body 2 and so on. The overall deformable nature of the tool is thus represented by an articulated object, each body constituting it being inflexible. As illustrated in Figure 2, bodies of index less than i have a relationship with the body C, and bodies of index greater than i have an affiliation relation with the body C,. The spherical connection Si is defined as the succession of three rotations 9x, 9 ~,, 9z, respectively about the axes xi, zi, in the reference point of the point P situated at the origin of the body C, and at the center of the articulation associated with it. Each spherical connection S1 (j = 1, ..., i, ..., N) thus determines the three degrees of freedom of the joint associated with each of the bodies Ci (j = 1, ..., i,. .., N) constituting the geometrical structure of the flexible tool. It will be noted that a local modification of the rotation angles 9x, 9y at the level of the spherical connections results in an overall deformation of the tool in bending, whereas the modification of the angle 9z generally results in a torsional deformation. The modification of the angular positions at rest of consecutive bodies makes it possible to represent the various forms of extremities encountered in reality. By fixing the length of each body, the rotation angles 9x, 9y, 9z at the spherical connection are initialized to specific values 0, nit, 9ynit, 9zinit to model the curves of the different ends. Thus, as illustrated by FIGS. 3a to 3f, it is possible to obtain a J-shaped right end (FIG. 3a) (FIG. 3b), an angulated end (FIG. 3c), Pig tail-shaped (FIG. pig in French) (figure 3d), in the shape of Simmons (figure 3e), or in the shape of Cobra (figure 3f). In a particular embodiment of the invention, the angle θZ1nit is initialized to a zero value because the endovascular tools considered do not have a helical shape. In the absence of constraints, the different shapes encountered can be defined by means of the initial angles 0, nit, 9ynit. 6.2.1 Mechanical properties of the MBML model It is firstly recalled that the elastic nature of a deformation of a rigid or flexible material can be defined by an elastic return (linear or not), allowing the material to recover its shape. origin at the lifting of stresses, and by a limit of elasticity, beyond which the material can no longer return to its original shape (it is called plastic deformation or rupture). In addition to the geometrical structure, the deformable behavior of a flexible tubular tool (for example a guide) is defined by specific intrinsic mechanical properties. We are interested here in the elastic deformation of the tool under constraints, by assuming that these constraints do not lead to plastic deformation or rupture. This elastic deformation is mainly determined by the characteristic flexibility / rigidity of the material. For the sake of clarity, we will speak later of the rigidity of the deformable structure, rigidity that can be higher or lower and give the tool a more or less great ability to deform and navigate in tortuous cavitary areas. The elasticity limit is transcribed in the MBML model by an angular limitation on each of the bodies. Thus the angles Ox, 0, of each spherical connection are limited to a maximum angle 6, T, ax in order to allow a maximum radius of curvature of the geometric structure of the tool or tools. As illustrated by FIG. 4a, for a given segment length, the increase of this angle 6, T, ax induces a more flexible behavior of the tool and increases the adaptability of its shape to the tortuosity of the structure. anatomical. Conversely, and as illustrated in Figure 4b, a low value of 6, T, ax results in a more rigid behavior of the tool.

In a particular embodiment, so that the deformation is admissible, in the sense of the elastic limit, an angular stress propagation mechanism specific to the invention is implemented. This propagation mechanism distributes the angular displacement, generated at the end of the tool in response to a collision, on different bodies of the model. Thus, when a collision is detected between a body (hereinafter referred to as the primary body) and the virtual structure (within which the model evolves), to cancel this collision, an angular displacement is effected at the level of the articulation of the body (hereinafter referred to as a secondary body) with a lower index than the primary body). The angle added to the current rotation angle must satisfy the constraint imposed by the maximum angle Bmax while ensuring the displacement. According to the invention, if the initial angular displacement does not make it possible to respect the constraint of the maximum angle at the articulation of the colliding body, then an angle distribution mechanism specific to the invention is implemented. . This distribution mechanism makes it possible to distribute a given angle on one or more bodies (hereinafter called tertiary body) of index lower than the secondary body, so that all the angles are admissible and that the resultant of the angular displacements applied is equal to the displacement angular initially specified. When an angle greater than amax is assigned to the articulation of a body, the link of the body, where the displacement is desired, is moved to its maximum allowed value Omax. The rest of the angle necessary to perform the rotation canceling the collision is propagated to the articulation of the father of the body considered, and iteratively to the other fathers so that all have their admissible stress and that the totality of the desired rotation is realized. hereinafter the angular displacement distribution algorithm. 3o.!. T: itu.: Fa i re.,. s p a a ag ag ag ag 7 7 7 7 7 7 7 7 s; If it is not possible, then if it is not possible to do so, if it is not possible The algorithm for angular stress propagation is given below: ## EQU1 ## The algorithm for angular stress propagation is given below: ## EQU1 ## t L <<:. '3 1+.' In a particular embodiment, in order to allow a body to be in a particular embodiment, it is possible for a body to to return to its initial configuration when it is no longer constrained, an elastic relaxation mechanism specific to the invention is implemented As illustrated in FIG. 5, restoring springs 50 are connected between the current positions and the The rest position P + 1 of a point P + 1 is expressed according to the initial angulation 9xinit, ~ ytntt, Oztntt.

relaxation process is defined by the equations of movement of the springs of restoration of the geometric structure. The spring force is a function of the stress and therefore of the rotation angles. It can express itself to a constant (which is integrated in the stiffness of the spring K) according to the angles 9x, 9y. The equation defining the movement of a stiffness restoration spring K connected between the virtual point P + 1 of angular coordinates TB ~ n ~ t = ~~ xtntt ~ ytntt, corresponding to the initial angulation and at rest, and the current point P + 1, of angular coordinates o '= is given by: Z mi 9 (t) = G + K (9 `(t) ù 9; nit) ù Y .0 (t) where K is the constant of stiffness of the spring, and y the damping coefficient. O is a force of penalty which makes it possible to ensure the localization of each body in the light. This force intervenes only in the event of a collision in order to force the body to move towards the central line of the anatomical structure. It is calculated by considering a spring of restoration, of stiffness KG, situated between the current point of angular coordinates O '=, 01T and the central line. Due to the nature of the geometric structure, the slightest displacement of a body causes a repercussion on all the son bodies. To limit this effect, the numerical integration, of the Euler type, is carried out with an integration step of low 0 (t + dt) = 8 i (t) + 8 i (t) dt

0 (t + dt) = 0 (t) + 0 (t). dt 6.2.2 Multilayer representation To establish a unified model allowing both the representation of a single tool, which can be of different natures (guide or probe), and the joint representation, that is to say say simultaneous, different tools (guide and probe), the notion of layer is introduced. According to the invention, a layer makes it possible to parameterize the intrinsic characteristics of each of the bodies of the model, and to determine their behavior during the simulation. In the particular case illustrated in FIG. 6, where the flexible navigation device comprises a guide and a probe, three types of layers are defined: a first single-tool layer 61 for the guide, a second single-tool layer 62 for the probe and a third multi-tool layer 63 for the combination of guide and probe tools. It is important to note that a body can not be affected simultaneously multiple layers. On the other hand, a model according to the invention can simultaneously comprise different layers. The set of parameters associated with a layer relates to characteristics of different natures, such as, for example, shape, rigidity and appearance. More specifically, the shape characteristic can, for example, define the radius R and the length L of the body, as well as the initial angles of rotation 9x '' "init 0init y 'z The stiffness characteristic can, for example, define the 9Tax maximum angle (associated with the body joint) and the elastic relaxation parameters K, KG, y and dt The appearance characteristic can, for example, define the color C and the type of visualization T.

It is noted that the parameters R, L and T are constant for the same layer. On the other hand, the shape (initial angles), stiffness (maximum angles) and elastic relaxation parameters can vary along the same layer. Thus, during the rise of a weakly rigid and curved end probe on a stiffer straight guide, the end of the probe is constrained by the guide whose characteristics are predominant at the multi-tool layer (guide and probe). , while the probe resumes its characteristics and its natural curvature within a single-tool layer when the guide is removed. The multi-tool parameters in question can be determined by retaining, for example, the lowest maximum angle, the highest damping coefficient and the stiffness constant of the single-hole layers, as well as zero initial angulation. However, the parameters of the multi-tool layer can also be obtained by a weighted combination of the parameters of the single-tool layers.

Depending on the type of layer or the value of the parameters of the layers, the geometric structure of the MBML model is decomposed into different parts in order to manage the different types of interactions involved in the catheterization simulation. As illustrated in FIG. 7, this decomposition is carried out at two levels.

At the level of the shape, there is formed part 71 where the bodies have a non-zero initial angulation (case of a non-right end), the right part 72 where the bodies have zero initial angulation. In the following, the term right end refers to the last body of the right part. At the level of the type of layer, there is the joint part 73 which groups together the bodies of the geometrical structure affected by the multi-tool layer and the free part 74 which groups the bodies affected only by one of the single-tool layers, those they can not be involved simultaneously in the free part. In the case of a catheterization simulation involving several tools, a switching of the layer type (mono-tool to multi-tool or vice versa) assigned to the bodies during the joint navigation of the two tools, modifies the distribution of the bodies between parts. spouse and free party. If all the bodies of the joint part do not have a zero initial angulation, this last part can be divided into a straight part and a formed part as well. 6.3 Method for managing the navigation of an MBML model A method for managing the navigation of an MBML model (as described above in paragraphs 6.1 and 6.2) is now described in connection with FIG. particular embodiment of the invention. As illustrated, the management method of the invention implements different types of interactions: the user / tool interactions El, initiator of the other interactions, which involve manipulations carried out by the user on the proximal part of the virtual tools ( such as, for example, a push, a pull, a rotation, etc.) by means of a man / machine interface (for example an alphanumeric keyboard, a 3D mouse, a microphone, etc.); - Tool / Tool E2 interactions, which refer mainly to the joint simulation of the evolution of several flexible tubular tools constrained by each other (partially integral with each other and sliding relative to each other). to the other). They involve the E21 update of the body parameters according to the type of layer associated with them, as well as the E22 self-collision management (that is, the collision of a tool with another tool) ; the E3 Tools / Tissue interactions, which concern on the one hand the E31 detection and the E32 management of collisions between the bodies of the MBML model and the virtual structure (which is for example the geometric representation of vascular structures), and on the other hand the management of the E33 deformations to be applied to the tools, both local E331 (that is to say at the level of a body) and global E332 (that is to say at the level of a set of bodies ) in response to a collision. 6.3.1 Tool / Fabric Interactions The manipulation of virtual tools by the user entails a modification of their forms within the anatomical virtual structure. The simulation is carried out under the assumption that the deformations of the vascular wall are negligible compared to the deformations undergone by the tools. The anatomical structure is supposed to be rigid. As mentioned earlier, the virtual tools are described by the MBML model. The anatomical structure is described by a precise surface mesh and a binarized volume. Extraction of the fine geometric description of complex vascular structures may, for example, be performed from patient data derived from a standard preoperative 3D TDM imaging examination using methods such as those described, for example, in [ Haigron, 04] and [Acosta, 05]. In addition to the E31 detection and collision E32 management functions, the E33 deformation loop involved in the simulation of the Tools / Tissue interactions involves E333 angular stress propagation and E334 elastic relaxation, as shown in Figure 9. collision In order to perform a simulation that complies with quasi-real-time constraints and to speed up the E31 collision detection process, which is generally expensive in terms of calculation time, a collision detection pipeline is implemented by means of three processes, namely: an approximate E311 detection process, an E312 proximity search process and an E313 exact detection process. As illustrated in FIG. 10, the exact detection E313 is based on the use of an orthographic virtual camera 80 associated with a body 2. More precisely, the optical center of the virtual camera 80 is located at the point of origin of the body 2 and its axis of sight is oriented along the principal axis of the body 2. This virtual camera 80, whose projection geometry is parallel, makes it possible to observe the scene in a field of view restricted to an enclosing volume. This volume is defined in a rectangular parallelepiped corresponding to the extrusion of a square, with sides the radius R of the body, between the planes noted Near and Far which are distant from each other by the length of the body L. Only the polygons between these planes are rendered by the virtual camera. The presence of polygons of the virtual vascular structure in the field of view of the virtual camera 80, implemented by means of hardware graphical functions, indicates an intersection between the body and the mesh describing the virtual structure, i.e. collision. In order to speed up collision detection and extend detection to other bodies in a global deformation process, the exact local E313 detection step is completed with an approximate E311 detection and E312 proximity search. The approximate detection E311 uses the binary volume describing the anatomical structure to determine whether a body is located inside or outside the arterial lumen delimited by the surface mesh. In the E312 proximity search, the initial surface mesh allowing a fine description of the virtual vascular structure (note that this fine description requires a large number of polygons) is decomposed according to a hierarchical approach such as that described, for example, in [ Lenoir, 06]. Each branch of the mesh (corresponding to a vascular branch) is decomposed into several segments described by a limited number of polygons. The high resolution mesh limited to the selected segment (s) is then exploited by the exact detection process E313. Collision Management Collision Management must provide the angular coordinates that are conducive to crash cancellation. These angular coordinates can be calculated in different ways by taking as input the intersected elements established during the exact detection. A calculation of the normals of the intersected vertices can be made. In order to keep the benefit of the exact detection carried out using graphic material, the implementation of a new graphic method (described below) is preferred. Of course, it is possible to consider implementing other graphical methods as long as they lead to calculations of angular coordinates. The management of E32 collisions is based on the use of a virtual perspective camera (not shown) such as that described, for example, in [Guilloux, 06]. This camera associated with a given body of the MBML model, implemented by means of hardware graphical functions, and having a cone of vision defined by the maximum angle 6, T, ax, is used to calculate a mobility map representing the set of the space accessible by this given body. The analysis of this map provides information characterizing the free space (orientation of the surface, depth of the light, ...) which are used in an angular search process E322 (also noted afterward RA) to determine the angular displacements aX, ay to be applied to the given body to cancel the collision. The angular displacement distribution algorithm is given below. Deformation Management The updating of the geometric structure of the MBML model (in other words its deformation in response to a collision) is based on the implementation of the E333 angular stress propagation and E334 relaxation processes. These processes take into account the results of E31 detection and collision E32 management. These processes are activated differently depending on the body considered on the geometric structure of the tool taking into account a more or less fine collision detection. To ensure that all bodies (that is, the source body and the body of the body) are covered by the following equation: the bodies of index lower than the source body) are well in the arterial lumen when a deformation is applied to the tool in order to cancel a collision on its end, the iterative process effectively implemented makes to intervene the different types of collision detection E311, E312 and E313, the angular search E322 and the elementary angular stress propagation E333 through an algorithm APCA + given below. f Z # the liY.ztai.lrf

where it is possible to use it; ~ ~ t. ki ': ~ .dr 1] .Z <3.Y Ltt r. ~ 1) .r oa} End If End I'iit C ~ ïAt.`

i air {"If 1cttl <ir_] 13 i, rr Ales:" Pi} Fiit If Si End For Fi3ii priieedlire.

The iterative process actually implemented to perform elastic relaxation is described by the Relaxation + algorithm given below. 22 rrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrr SI + (t 1;,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,. . i. '}) irrtirat {? t. d [. ~ tt'F, t., I: r -} r ..:. shot [v,] tr. .v rt [:]; "". ' : sr i> .. ['] + ts>',: tt tt.r ': ~.: F [.`:] I rta: Yr jr]:' F * tr [': I}, rt {'i.] ~ t`sc + Freight Ct: t.' ['..]. - file. .a. ~ - .. ir` * t. 25: End. P (nurhie i'-azt ~ r1 .tri. ': ~' ~. ~ It ~.:;: 27 Fin. '~' .Irii ~, i- F ... The elastic relaxation is applied from the oldest body to the distal end of the tool in order to know the position of a body with respect to the light (ie the area of free space) and to calculate the penalty force, an approximate collision detection E311 is performed at each iteration.To avoid that an angle value is greater than the angle Omax, the value of the angle and speed can be reset prior to integration, and an additional force can be added to the spring motion equation to constrain the model, and any residual collisions are treated upon relaxation. by the APCA + procedure (described above) re-applied to all displaced bodies if an exact collision is detected APCA + and Relaxation procedures + are executed consecutively on a body or a set of bodies in order to manage two types of deformations: - local deformation: when carrying out an action of type displacement or update of a layer on a given body, this action can result a collision locally to the given body. This collision is then canceled by means of a local deformation algorithm DL given below; global deformation: in response to a collision, the displacement of a given body can cause a displacement on all bodies of index higher than the given body, thus causing simultaneous collisions on different points of the mesh representing the virtual anatomical structure. The global deformation loop DG is able to manage several collisions while guaranteeing the speed of convergence of the simulation. The global deformation algorithm DG is given below. It is important to note that at this stage, because no body is added to the geometric structure of the tool, the exact detection performed in the APCA + and Relaxation + loops does not imply a prior proximity search. that is to say a search of the anatomical segment. 6.3.2 Tool / Tool Interactions Tool / tool interactions are introduced when it is necessary to update the body parameters, either to simulate the advancement of a tool during joint navigation, or to represent the properties. the heterogeneity of the tools. Self-collision cases also belong to tool / tool interactions. These occur when the tools collide with themselves. With the exception of the rigidity that can evolve along a layer during the navigation of tools, the other parameters affecting the behavior of the tool (radius, initial angulation, ...) are exclusively updated when a body switches from a single-tool layer to a multi-tool layer, and vice versa. This switching thus involves different updates made simultaneously. Update processes apply here locally, only the parents of a given body (ie bodies with subscript below the given body) are affected. Displacements generated on the child bodies (that is to say bodies with a subscript greater than the given body) and the global update of the model during the navigation are processed at the level of management of user interaction tools. In the same way, it is only a question here of deformations related to the update of the parameters.

The real-time update of the stiffness parameters is performed at the level of the angular propagation (angle 6, T, ax) and the elastic relaxation (dt, y, KG and K). The angular update may imply a new constraint, for example, for a new value 6, T, ax, lower than the old value, the angles ex, 0y may no longer satisfy the new angular constraint. In the latter case, the angle or angles greater than emax are associated with this maximum value so that the constraint is satisfied. An eventual collision is then managed by a local deformation DL to the body considered. The algorithm for updating the angular stress is given below. It is noted that the updating of the relaxation parameters does not directly cause a constraint because they always intervene after an angular propagation. Their updating does not therefore require immediate deformation to satisfy a constraint.

In a particular embodiment, the update of the radius of a given body occurs when switching from one layer to another. If the new radius Rnew is smaller than the old radius Raid, the body is relaxed in order to move in contact with the arterial wall. On the other hand, if Rnew is superior to Rosa, a local deformation DL is made on the body to cancel a possible collision. The algorithm for updating the radius of a body is given below. The update of the initial angulation necessarily involves a displacement when it is not equal to the previous one. In case of displacement, DL local deformation is always performed. During a layer switch, for example, when the parameters of a body take the values of a new layer, all the previous updates are performed simultaneously. Local deformations or relaxations are performed only once if they are necessary according to the cases described previously. In addition to tool update functions, tool / tool interactions also affect auto-collision detection. FIG. 11 illustrates a self-collision between a first body 91 and a second body 92. The strong interdependence between consecutive bodies of the MBML model can be exploited to accelerate the detection of self-collision cases by using the following two criteria: - two bodies can not collide if the natural curvature of the model does not allow it; - two bodies can not collide if they are not in the same segment of the mesh describing the anatomical surface.

The curvature of a set of bodies is limited by the maximum angle umax of each of them. Each body can thus know the potential collisions with the bodies of his descendants (his sons) or of his ancestry (his fathers) sharing with him a segment of the mesh. From the oldest body (ie body of index lower than the primary body) in a segment, the maximum angles umax of the consecutive bodies are cumulated up to the youngest body (ie body of index superior to the primary body) in the segment considered. Under these conditions, a self-collision can exist if the sum of the maximum angles is greater than 180 °. In this case, the graphic hardware functions E321 are used to render the oldest body instead of the segments of the anatomical surface, and to detect the collision. This collision is managed by applying DL local deformation to the youngest bodies to limit the number of displaced bodies. An overall deformation DG is then made from the displaced body to the right end of the model. 6.3.3 User / Tool Interactions User / Tool interactions cause Tool / Tool interactions when a tool is manipulated with respect to another tool, and then Tools / Tissue interactions when the tool being manipulated deforms as a result of a collision. The behavior of the tool is directed by the reactions of its end. When this is constrained by the vascular structure, the tool bends. Following a new manipulation, it can be released. The tool stiffens and then takes the minimum curvature. The management of user / tool interactions consists of postponing the action performed by the user on the distal end of the tool being manipulated, and not applying this action directly to the insertion point of the model. Managing these interactions may involve different procedures if the user interacts with a free tool or if he or she interacts with a sliding tool on another tool. We will then speak of free navigation when the user's interactions apply to the free part of the model (single-tool layer) and of joint navigation when they apply to the joint part (multi-tool layer). In all cases, only one tool is handled at a time.

Translation of a tool (push and pull) When the manipulated tool has a free part, the simulations of the push-forward and pull-back of the tool are translated respectively by adding and removing a body. In the particular embodiment illustrated in Figure 12, the thrust of the guide results in the addition of a body 900 at the right end of the model. When the manipulated tool slides on another tool and has no free part, the simulations of the thrust and the withdrawal of the tool result in the change of layer of one of the bodies located on either side of the end of the joint part This tool translation operation requires an update of the rigidity parameters of the tool which is heterogeneous in nature and involves a repositioning of the tool in the light or the cavity by a deformation local DL or global DG. Thus the simulation of a translation of the tool can be summarized by the following two steps: - update of the stiffness parameters related to the heterogeneity of the tool; - model distortion caused by adding, removing or changing a body layer. Updated rigidity A tool is considered heterogeneous when it is composed of parts of distinct rigidities (usually two or three for a guide). During navigation, these different parts must move in accordance with the manipulation performed. This one is translated at the level of the bodies by the update of body in body of rigidity. This propagation is performed at a given layer. The update is necessary only for the bodies situated at the border between two parts of different rigidities of the given layer. Each of these parts of homogeneous rigidity is described by a precise number of bodies. The updating of the rigidities, of the same layer, is applied to the bodies located between two parts of different rigidities. For the joint part, the update is performed on a single-tool layer, which involves the re-calculation of the parameter values corresponding to the multi-tool layer. As shown in Figure 13, the rigidity update process starts from the Pi insertion point of the model. From this body, the first boundary between the body C; and the body C 1 +1 of different stiffness for the manipulated layer is sought. Two parts of distinct rigidity are thus defined, the first between Co and C; the second between C; +1 and C; + n. For the thrust, the rigidity of the son body C; +1 is updated with that of C. The reverse for the withdrawal where the body C; is updated with the stiffness of C; +1. If an update of the rigidity caused a displacement, a global deformation DG is made on all the bodies between C; +2 and C; + n for the thrust (C; +1 having already been treated), or C; +1 and C; - 1 for removal (C; + n being processed by the next update or the next step removed). This deformation restores the bodies in the light. If the right end is not reached, the same process is repeated at this boundary between C; + n and C; + n + 1 iteratively until C; + n is the last body of the right end of the model. The algorithm of the evolution of the rigidity along a given layer is given below. with an inner jouissance when f) t "x {irid ic: e .: the f 11 Fiiÿi: 4 ,. ri] i For the 1 xced 1, 2. '' '' '' '' '' '' '' '' '' '' '' '' '' '' '' '' '' '' '' '' '' '' '' '' '' '' '' '' '' '' '' '' '' '' '' '' '' '' '' '' '' '' '' '' '' '' '' '' '' '' '' '' '' '' '' '' '' '' '' '' '' '. ti lih a rrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrn o.> {1] Make:) E7. @ tl {'li3rji) i #. + of .at2 .IF.iT-ëii 4 dldf i} fe: + the #' 3irt ii it: i: y: l ? E7Srt iii {`In. I> rocecl.11re For [T \ IISE S HI .a. Eu. ~ 32 dr lt hrnrn Free navigation As illustrated in Figure 14a, the simulation of a translation manipulation of the tool is accomplished by adding or removing a body at the right end of the model corresponding to the body 1001 index I. The thrust of the tool results in the addition of a body 1002. This new body 1002 of index i + 1 has the parameters of its father (body 1001) corresponding to the layer of the pushed tool. proximity is then performed on the new body 1002 and the formed part of the model then makes it possible to affect the mesh segments for the collision detection. The collisions are then sought on the bodies 1004 and 1005 corresponding to the formed end and the last body 1002 introduced. On these same bodies, a global deformation DG is executed if a collision is detected. In the absence of formed end, the deformation is local at the right end and no longer global (only a body is treated). The number N of fathers affected by the deformation caused by the addition of this body is saved to be reused during the simulation of the withdrawal. In contrast to the thrust, and as shown in FIG. 14b, the simulation of the withdrawal subtracts the last body 1001 from the right end of the model. The body 1003 then becomes the last body of the right end of the model. The angle 9z of the removed body is added to that of his father so that this withdrawal does not affect the orientation of the formed end. The number N of fathers affected by the addition of the body of index i is reused to simultaneously relax all fathers at the formed end. Joint Navigation In the embodiment illustrated in Figure 15, to simulate the thrust, the son 1020 of the body 1010 of the end of the joint portion passes from the single-tool layer to the multi-tool layer. For the withdrawal, the body 1010 of the end of the joint part switches from the multi-tool layer to the single-tool layer. The single-tool layer used is that of the uncooled tool.

For the manipulation of the probe, the fixed tool is the guide and vice versa for the manipulation of the guide. A global deformation DG is then performed on the new free part. Rotation of the tool In the rest of the description, it is assumed that there is no torque effect. Thus, it is only in the presence of a formed part that a rotation has an influence on the geometric structure of the model. The entire rotation performed by the user is rendered on the unconstrained end of the free part. This set of unconstrained bodies is identified by the bodies which, from the right end, are not in contact with the vascular wall of the virtual structure. At first, from the right end, the body being entered the last collision is searched. The unconstrained part of the model is therefore located between the son of this body and the end. The desired angle of rotation is added to the angle at 9z of this son. When the right end is in contact with the vascular wall of the virtual structure, the desired angle of rotation is assigned to the first body of the formed end. Finally, a DG global deformation process is performed on all the body bodies of the affected body. 6.3.4 Examples of Catheterization Simulations Figures 16a to 16d present examples of simulation and navigation of flexible instruments within tubular structures. The tubular structures considered are vascular structures whose geometrical description was obtained from the standard preoperative imaging examination, namely X-ray CT. The number of polygons used for the description of the vascular meshes varies from 11172 to 68112. for complete aortoiliac structure. FIG. 16a illustrates an example of a navigation simulation of two tools 2002 and 2003 of homogeneous characteristics and of different rigidities, within an iliac artery 2001. FIG. 16b illustrates an example of a navigation simulation of two 30 tools 2005 and 2006 of homogeneous characteristics, of the same rigidities, and of different radii (the radius of the tool 2006 is greater than that of the tool 2005), within an iliac artery 2004. Figure 16c illustrates an example of navigation simulation a homogeneous tool 2008 and a heterogeneous tool 2009 including a flexible end 2010, within an iliac artery 2004. Figure 16d illustrates an example of navigation simulation of a homogeneous tool 2020 and two heterogeneous tools 2030 and 2040 used together in an iliac artery 2050. In the case of the joint simulation, the tools 2030 and 2040 of different rigidities slide relative to each other. 10 APPENDIX 1 Acosta O, Goksu G, Lucas A, Kulik C, Rolland Y, Haigron P. Geometrical description of anatomical structures based on virtual exploratory navigation. Surgetica; 2005; Grenoble, France; 2005. p.437-45.

Anderson, H., Chui, C., Cai, Y., et al (2002). Virtual reality training in interventional radiology. In Thieme Medical Publishing, N. Y., Editor, Seminars in Interventional Radiology, Vol. 19, pp. 179-184.

Analytical guide wire motion algorithm for simulation of endovascular interventions. K. Konings, B. van de Kraats, T. Alderliesten and W. J. Niessen. Medical and Biological Engineering and Computing, Volume 41, Number 6 / November 2003

Suraj Bhat, Thenkurussi Kesavadas, and Kenneth R. Hoffmann (2005). A physically-based model for guidewire simulation on patient-specific data. Volume 1281, May 2005, Pages 479-484 CARS 2005: Computer Assisted Radiology and Surgery [Guilloux, 06] Guilloux V, Haigron P, Goksu C, Kulik C, Lucas A. Simulation of guide-wire navigation in complex vascular structures. Proceedings of SPIE Medical Imaging 2006: Visualization, Image-Guided Procedures, and Display; 2006; San Diego, USA: SPIE, Bellingham, WA; 2006. 6141: 11 p. [Haigron, 04] Haigron P, Bellemare ME, Acosta O, Goksu C, Kulik C, Rioual K., Lucas A. Depth-map-based analysis for active navigation in virtual angioscopy. IEEE Transactions on Medical Imaging. 2004; 23 (11): 1380-1390.

[Daswon, 00] S Dawson, S Cotin, D Meglan, D W Shaffer, M A Ferrell. (2000). Designing a computer-based simulator for interventional cardiology training. Catheter Cardiovasc Interv. 2000 Dec; 51 (4): 522-711108693 (P, S, E, B)

[Cotin, 05] Stephane Cotin, Christian Duriez, Lenoir Julien, Paul F. Neumann, Steven Dawson: New Approaches to Catheter Navigation for Interventional Radiology Simulation. MICCAI (2) 2005: 534-542.

45 [Lenoir, 06] Lenoir, J., Cotin, S., Duriez, C., and Neumann, P. (2006). Interactive physically-based simulation of catheter and guidewire. Computer & Graphics, 30 (3): 417-423. [Acosta, 05] [Anderson, 02] [Konings, 03] [Bhat, 05] [Lawton, 99] Lawton, W., Raghavan, R., Ranjan, S., and Viswanathan, R (1999) .Ribbons and groups: a thin rod theory for catheters and filaments Journal of Physics A: Mathematical and General, Volume 32, Number 9, 1999, pp. 1709-1735 (27)

Claims (17)

REVENDICATIONS1. A method of generating an editable model of a flexible navigation device comprising at least one tool, said model being able to navigate within a virtual structure described by a surface mesh, said method comprising a step of obtaining a plurality body by discretization of said device, each body comprising a hinge for linking said body to another body, characterized in that said method comprises, for each body, a step of association with said body of a modifiable layer representative of a set of parameters relating to at least one tool of said device. 2. Generation process according to claim 1, characterized in that said set of parameters comprises at least one parameter belonging to the group comprising: mechanical parameters of at least one given tool; - shape parameters of at least one given tool; - Visualization parameters of at least one given tool. 3. Generation process according to any one of claims 1 and 2, characterized in that each body is a rigid cylinder. 4. Generation process according to any one of claims 1 to 3, characterized in that it comprises, for each articulation, a step of association with said articulation of at least one determined angular constraint. 5. Modifiable model of a flexible navigation device comprising at least one tool, said model being able to navigate within a virtual structure described by a surface mesh, said model comprising a plurality of bodies, each body comprising a hinge allowing to link said body to another body, characterized in that each body is associated with a modifiable layer representative of a set of parameters relating to at least one tool of said device. A storage medium containing at least one modifiable model of a flexible navigation device comprising at least one computer-readable tool generated according to the generation method according to at least one of Claims 1 to 4, said model comprising a plurality of body, each body comprising a hinge for linking said body to another body, characterized in that each body is associated with an modifiable layer representative of a set of parameters relating to at least one tool of said device. 7. Computer program product downloadable from a communication network and / or recorded on a computer readable medium and / or executable by a processor, characterized in that it comprises program code instructions for the implementation of the method of generating an editable model according to at least one of claims 1 to 4, when said program is run on a computer. 8. A method for managing the navigation of an editable model of a flexible navigation device comprising at least one tool, said model being able to navigate within a virtual structure described by a surface mesh, said model comprising a plurality of bodies each body being identified by an index number, each body comprising a hinge allowing said body to be linked to another body, characterized in that it comprises the following steps: obtaining an modifiable model, called an initial model, comprising a plurality of bodies each associated with a modifiable layer representative of a set of parameters relating to at least one tool of said device; - obtaining a navigation command; - Generation of a modified model, by modifying said initial model according to a modification operation selected from a plurality of modification operations according to said navigation command. 9. Management method according to claim 8, characterized in that said plurality of modification operations comprises an operation belonging to the group comprising: an operation of modifying a body of said initial model by modifying the modifiable layer associated with said body; an operation of inserting a new body into said initial model; an operation of deleting a body of said initial model; an operation of rotation of said initial model around its axis. 10. Management method according to any one of claims 8 and 9, characterized in that it comprises, for each articulation, a step of association with said articulation of at least one determined angular stress. 11. Management method according to any one of claims 8 to 10, characterized in that it comprises a step of detecting in said modified model of at least one body colliding with said virtual structure and / or with another body , and in that, for each colliding body, an angular stress propagation phase is carried out. 12. Management method according to claim 11, characterized in that said angular stress propagation phase comprises the following steps: determination of a first collision cancellation angle; applying said first collision cancellation angle to the articulation of said colliding body, said body being treated; checking that the articulation of said treated body satisfies said at least one angular constraint associated therewith; in the case of negative verification: applying a second angle to the articulation of said treated body, said second angle allowing the articulation of said treated body to reach said at least one angular constraint; O determining a body to be treated, linked to said treated body and having an index number lower than that of said treated body; o determining a third angle from said second angle and said first collision cancellation angle; o applying said third angle to the articulation of said body to be treated, said body to be treated becoming the treated body before returning to the verification step. 13. Management method according to claim 12, characterized in that it comprises a relaxation phase comprising the following steps: - determination of a fourth relaxation angle; for each treated body, application of said fourth relaxation angle to the articulation of said treated body. 14. The method of claims 8 to 13, characterized in that it comprises a step of detecting at least one block of one or more tools in said virtual structure. 15. A computer readable storage means, storing a set of instructions executable by said computer to implement the management method according to at least one of claims 8 to 14. 16. Computer program product downloadable from a communication network and / or recorded on a computer readable medium and / or executable by a processor, characterized in that it comprises program code instructions for executing the steps the management method according to at least one of claims 8 to 14, when said program is run on a computer. 17. Device for managing the navigation of an editable model of a flexible navigation device comprising at least one tool, said model being able to navigate within a virtual structure described by a surface mesh, said model comprising a plurality of bodies each body being identified by an index number, each body comprising a hinge for linking said body to another body, characterized in that said management device comprises: means for obtaining an editable model, said initial model, comprising a plurality of bodies each associated with a modifiable layer representative of a set of parameters relating to at least one tool of said flexible navigation device; means for obtaining a navigation command; means for generating a modified model making it possible to modify said initial model according to a modification operation chosen from among a plurality of modification operations according to said navigation command; .5