FR3148899A1 - Method for determining the parameters for fitting a prosthesis to a patient's joint - Google Patents

Abstract

The present invention relates to a method for determining fitting parameters of a prosthesis on a patient's joint, the method being characterized in that it comprises the implementation by data processing means (11) of a server (1) of steps of: Obtaining a kinematic model of said joint before fitting the prosthesis, called the preoperative kinematic model; Building a kinematic model of said joint after fitting the prosthesis, called the postoperative kinematic model, for current values of the fitting parameters of said prosthesis, by modifying said preoperative kinematic model; Predicting the postoperative values of a set of functional metrics of said joint based on said postoperative kinematic model; Validating or not the current values of the fitting parameters of said prosthesis based on said predicted postoperative values of the set of functional metrics; If the current values of the fitting parameters of said prosthesis are not validated, modifying the current values of the fitting parameters of said prosthesis, updating the model postoperative kinematics, then repeating steps (c) and (d) based on the updated postoperative kinematic model. [Fig. 2]

Description

Method for determining the parameters for fitting a prosthesis to a patient's joint

GENERAL TECHNICAL FIELD

The present invention relates to the field of biomechanics. More specifically, it relates to a method for determining parameters for fitting a prosthesis to a patient's joint.

STATE OF THE ART

A joint prosthesis is an internal implant (endoprosthesis) that replaces the defective surfaces of a joint, with the aim of allowing, among other things, stable support, flexion and extension, and relieving pain. The most common example is the knee prosthesis, but there are also many hip, shoulder, etc. prostheses.

Knee prosthetic surgery has thus seen a rapid evolution in practices, moving from an essentially bone-based surgery to a surgery capable of taking into account the peripheral soft tissues in order to guarantee prosthetic longevity and a good quality of life for the patient. Nevertheless, more than 20% of patients say they are dissatisfied, mainly due to persistent pain and the inability to resume a certain number of daily life activities.

This high rate of patient dissatisfaction is largely explained by the inadequacies of certain surgical protocols, for example in taking into account the balancing of tensions in the peripheral ligament structures of the knee and in particular the external and internal collateral ligaments, or in taking into account post-operative patellar kinematics during flexion extension.

Thus, the document K. A. Gustke, GJ Golladay, MW Roche, GJ Jerry, LC Elson, CR Anderson, “Increased satisfaction after total knee replacement using sensor-guided technology”, Bone Joint J 2014;96-B:1333–8, October 2014 shows that the rate of patient dissatisfaction goes from 21.1% to 3.3% when the surgeon takes into account ligament balance in his protocol.

The problem is that taking into account soft parts such as ligamentous structures, or for example in the case of the knee the patellar race, during interventions on joints involves very complex personalized biomechanical considerations to guarantee the precision of the surgical gesture.

• Certains fabricants se concentrent sur le design d’inserts en polyéthylène (notamment pour le plateau tibial prothétique) afin de maximiser la congruence entre les implants et ainsi stabiliser l’articulation. Cette approche pallie en partie et seulement indirectement les insuffisances de l’équilibrage ligamentaire.
• Des stratégies opératoires (parfois robotisées) dites « bi-uni » permettent la pose des deux côtés de l’articulation de prothèses unicompartimentales (qui normalement ne recouvrent qu’un coté – médial ou latéral du genou) afin de préserver les structures molles et par là même la stabilité de l’articulation. Ce n’est malheureusement pas toujours possible.
• La robotique peropératoire permet d’assister le chirurgien dans la mesure des espaces intra-articulaires en extension et en flexion afin d’équilibrer la tension bilatérale des ligaments collatéraux. Cette mesure ne peut cependant être faite qu’après la réalisation de la première coupe osseuse (tibiale en général) ce qui en limite les bénéfices.

To take the example of ligament balancing, many avenues have been explored to more easily integrate these aspects into informed therapeutic decision-making:

• Some manufacturers focus on the design of polyethylene inserts (especially for the prosthetic tibial plateau) in order to maximize the congruence between the implants and thus stabilize the joint. This approach partially and only indirectly compensates for the inadequacies of ligament balancing.
• Surgical strategies (sometimes robotic) called "bi-uni" allow the placement of unicompartmental prostheses on both sides of the joint (which normally only cover one side - medial or lateral of the knee) in order to preserve the soft structures and therefore the stability of the joint. Unfortunately, this is not always possible.
• Intraoperative robotics can assist the surgeon in measuring the intra-articular spaces in extension and flexion in order to balance the bilateral tension of the collateral ligaments. However, this measurement can only be made after the first bone cut (usually tibial) has been made, which limits its benefits.

1. qui prenne en compte la morphologie du patient avec précision,
2. qui permette de simuler fidèlement la cinématique de l’articulation du patient,
3. qui propose des paramètres de pose de la prothèse guidant le chirurgien vers la meilleure option pour le patient, et
4. que le chirurgien puisse utiliser le plus tôt possible au cours de l’intervention chirurgicale afin d’éviter les gestes tels que les coupes osseuses sur lesquels il n’y a pas ou peu de retour possible en cas de changement de planning.

Existing techniques are therefore insufficient, and it remains desirable to obtain a surgical planning process:

1. which takes into account the patient's morphology with precision,
2. which allows the patient's joint kinematics to be faithfully simulated,
3. which offers prosthesis placement parameters guiding the surgeon towards the best option for the patient, and
4. that the surgeon can use as early as possible during the surgical procedure in order to avoid procedures such as bone cuts on which there is little or no way back possible in the event of a change in schedule.

The invention improves the situation.

PRESENTATION OF THE INVENTION

1. Obtention d’un modèle cinématique de ladite articulation avant pose de la prothèse, dit modèle cinématique préopératoire ;
2. Construction d’un modèle cinématique de ladite articulation après pose de la prothèse, dit modèle cinématique postopératoire, pour des valeurs courantes des paramètres de pose de ladite prothèse, en modifiant ledit modèle cinématique préopératoire ;
3. Prédiction des valeurs postopératoires d’un ensemble de métriques fonctionnelles de ladite articulation en fonction dudit modèle cinématique postopératoire ;
4. Validation ou non des valeurs courantes des paramètres de pose de ladite prothèse en fonction desdites valeurs postopératoires prédites de l’ensemble de métriques fonctionnelles ;
5. Si les valeurs courantes des paramètres de pose de ladite prothèse ne sont pas validées, modification des valeurs courantes des paramètres de pose de ladite prothèse, mise à jour du modèle cinématique postopératoire, puis répétition des étapes (c) et (d) sur la base du modèle cinématique postopératoire mis à jour.

The present invention therefore relates, according to a first aspect, to a method for determining parameters for fitting a prosthesis to a patient's joint, the method being characterized in that it comprises the implementation by data processing means of a server of steps of:

1. Obtaining a kinematic model of said joint before fitting the prosthesis, called a preoperative kinematic model;
2. Construction of a kinematic model of said joint after fitting of the prosthesis, called postoperative kinematic model, for current values of the fitting parameters of said prosthesis, by modifying said preoperative kinematic model;
3. Prediction of postoperative values of a set of functional metrics of said joint based on said postoperative kinematic model;
4. Validation or not of the current values of the fitting parameters of said prosthesis according to said predicted postoperative values of the set of functional metrics;
5. If the current values of the fitting parameters of said prosthesis are not validated, modification of the current values of the fitting parameters of said prosthesis, updating of the postoperative kinematic model, then repetition of steps (c) and (d) on the basis of the updated postoperative kinematic model.

According to advantageous and non-limiting characteristics:

Step (a) comprises a sub-step (a1) of obtaining at least one three-dimensional medical image of said joint; and (a2) of constructing said preoperative kinematic model from said three-dimensional medical image of said joint.

Substep (a2) comprises identifying the bony surfaces of said joint in said three-dimensional medical image of said joint.

The said preoperative kinematic model is constructed by finite element biomechanical simulation or by geometric biomechanical simulation from the shapes of the bone surfaces of the said joint identified.

Said preoperative kinematic model is constructed by geometric biomechanical simulation from the shapes of the bone surfaces of said identified joint, step (b) comprising the modification of the shapes of the bone surfaces of said joint, for the current values of the fitting parameters of said prosthesis, and construction of said postoperative kinematic model by geometric biomechanical simulation from the modified shapes of the bone surfaces.

Step (a1) comprises acquiring said three-dimensional medical image of said joint by a medical imaging device.

Step (d) compares the predicted postoperative values of the functional metric set and the target values of the functional metric set.

Step (a) comprises a step (a3) of estimating the preoperative values of said set of functional metrics of said joint based on said preoperative kinematic model, said target values being the estimated preoperative values.

The current values of the fitting parameters of said prosthesis are validated when they minimize a cost function comparing the predicted postoperative values and the target values of the set of functional metrics, the current values of the fitting parameters of said prosthesis being modified in step (e) by a gradient descent type algorithm on said cost function.

Said set of functional metrics defines a ligament balance of said joint, the functional metrics being in particular profiles of variation of the lengths of the ligaments of said joint, called anisometries.

The said cost function is , Or And are respectively the preoperative and postoperative lengths of the i-th ligament of said joint for an angle α of flexion of said joint.

• Obtenir un modèle cinématique de ladite articulation avant pose de la prothèse, dit modèle cinématique préopératoire ;
• Construire un modèle cinématique de ladite articulation après pose de la prothèse, dit modèle cinématique postopératoire, pour des valeurs courantes des paramètres de pose de ladite prothèse, en modifiant ledit modèle cinématique préopératoire ;
• Prédire des valeurs postopératoires d’un ensemble de métriques fonctionnelles de ladite articulation en fonction dudit modèle cinématique postopératoire ;
• Valider ou non les valeurs courantes des paramètres de pose de ladite prothèse en fonction desdites valeurs postopératoires prédites de l’ensemble de métriques fonctionnelles ;
• Si les valeurs courantes des paramètres de pose de ladite prothèse ne sont pas validées, modifier les valeurs courantes des paramètres de pose de ladite prothèse, mettre à jour le modèle cinématique postopératoire, puis répéter les étapes consistant à prédire les valeurs postopératoires d’un ensemble de métriques fonctionnelles de ladite articulation, et valider ou non les valeurs courantes des paramètres de pose de ladite prothèse, sur la base du modèle cinématique postopératoire mis à jour.

According to a second aspect, the invention relates to a server for determining parameters for fitting a prosthesis to a patient's joint, characterized in that it comprises data processing means configured to:

• Obtain a kinematic model of said joint before fitting the prosthesis, called a preoperative kinematic model;
• Construct a kinematic model of said joint after fitting of the prosthesis, called postoperative kinematic model, for current values of the fitting parameters of said prosthesis, by modifying said preoperative kinematic model;
• Predicting postoperative values of a set of functional metrics of said joint based on said postoperative kinematic model;
• Validate or not the current values of the fitting parameters of said prosthesis based on said predicted postoperative values of the set of functional metrics;
• If the current values of the pose parameters of said prosthesis are not validated, modifying the current values of the pose parameters of said prosthesis, updating the postoperative kinematic model, then repeating the steps of predicting the postoperative values of a set of functional metrics of said joint, and validating or not the current values of the pose parameters of said prosthesis, on the basis of the updated postoperative kinematic model.

• Obtenir depuis ledit dispositif d’imagerie médicale au moins une image médicale tridimensionnelle de ladite articulation ;
• Construire ledit modèle cinématique préopératoire à partir de ladite image médicale tridimensionnelle de ladite articulation.

According to a third aspect, the invention relates to a system comprising a server according to the second aspect and a medical imaging device, the data processing means being further configured to:

• Obtaining from said medical imaging device at least one three-dimensional medical image of said joint;
• Construct said preoperative kinematic model from said three-dimensional medical image of said joint.

According to a fourth and a fifth aspect, the invention relates to a computer program product comprising code instructions for executing a method according to the first aspect of determining parameters for fitting a prosthesis on a joint of a patient; and a storage means readable by computer equipment on which is recorded a computer program product comprising code instructions for executing a method according to the first aspect of determining parameters for fitting a prosthesis on a joint of a patient.

PRESENTATION OF FIGURES

Other features and advantages of the present invention will become apparent from the following description of a preferred embodiment. This description will be given with reference to the appended drawings in which:

there is a diagram of a system for implementing the method according to the invention;

there is a flowchart illustrating the steps of an embodiment of the method according to the invention;

there represents a view of the internal posterior condyle of the femur bearing the trace of the point of contact of the tibia on the femur during flexion in an example of construction of a preoperative kinematic model by geometric biomechanical simulation;

there represents the discretization of the open contour Γ defining said trace of the point of contact of the tibia on the femur during flexion of the ;

there represents an example of a postoperative kinematic model in which we see the prosthesis in place and the ligaments (the 3 fibers of the internal collateral ligaments are deliberately represented above the bone);

there is a graph representing the estimated preoperative anisometries for an example joint when said preoperative kinematic model is constructed by finite element biomechanical simulation;

there is a graph representing the estimated preoperative anisometries for said example joint when said preoperative kinematic model is constructed by geometric biomechanical simulation (used for the following figures);

there is a graph representing the predicted postoperative anisometries for said example joint for the postoperative kinematic model constructed for the initial values of the fitting parameters of said prosthesis;

there is a graph representing the predicted postoperative anisometries for said example joint for the postoperative kinematic model constructed for the determined optimal values of the fitting parameters of said prosthesis.

DETAILED DESCRIPTION

Architecture

• Extension/flexion de la jambe sur la cuisse (environ 160° d’amplitude) ;
• Rotation interne/externe de la jambe sur la cuisse (environ 20° d’amplitude genou fléchi) ;
• Translation antéro-postérieure du plateau tibial (environ 10 mm d’amplitude au cours du mouvement d’extension/flexion).

The present invention relates to a method for determining parameters for fitting a prosthesis to a patient's joint in a system as shown in the . The articulation, or joint, is an anatomical element of the patient's body forming a junction zone between a plurality of bony ends and forming at least one degree of freedom. Said articulation 1 is typically the knee (which involves the femur, the tibia and the patella), but it can also be the hip, the ankle, the elbow, the wrist, the shoulder, etc. In particular, the articulation can take a posture (or pose) among a plurality of possible postures, typically defined by one or more parameters - called “degrees of freedom” - such as angles each corresponding to a possible movement of the articulation. For example, the knee can thus produce the following movements:

• Extension/flexion of the leg on the thigh (approximately 160° range);
• Internal/external rotation of the leg on the thigh (approximately 20° range of motion with the knee bent);
• Antero-posterior translation of the tibial plateau (approximately 10 mm amplitude during the extension/flexion movement).

In the remainder of this description, the example of the knee extension/flexion movement will be taken, but those skilled in the art will be able to transpose the invention to other joints and other movements.

The prosthesis concerned is typically a total knee prosthesis, known as TKR.

By “prosthesis fitting parameter” is meant broadly any numerical parameter that allows the final result to be defined after fitting the prosthesis in the joint during a surgical procedure on said joint, in particular a thickness, a position, an angle, an offset, etc. These parameters are “internal”, i.e. relating to the choice and design of the prosthesis (for example a thickness, a parameter can even be the identifier of a prosthesis model among several possible models), and/or “external”, i.e. relating only to the fitting conditions, independently of the design (for example an offset). This is also referred to as “planning”.

For example, in the case of a PTG, these installation parameters are for example the following: thicknesses of the distal and posterior resections, axial rotations, frontal rotations in varus or valgus, posterior slopes, and other possible offsets according to the three axes.

Naturally, each prosthesis will have its own fitting parameters and the person skilled in the art will be able to apply the present invention to any prosthesis of any joint with any fitting parameter of choice. It is also entirely possible to manually determine certain fitting parameters, and therefore to apply the present invention only to certain other parameters.

The present method is implemented by a server 1 having data processing means 11 (typically a processor), and generally data storage means 12 (a memory, for example a hard disk) and an interface 13 (for example a screen, a keyboard, an input port, etc.).

Preferably, a medical imaging system 10 is also applied for acquiring medical images of said joint.

This system 10 can be directly or indirectly (for example via a network 20 such as the Internet) connected to said server 1 so that the latter is capable of receiving said medical images. The interface 13 of the server 1 can further serve as an interface of the system 10 (to control it and obtain the acquired medical images).

Said medical images are typically volumetric 3D images, possibly reconstructed from 2D sections, i.e. tomograms or “CT-scans” (the system 10 is typically an X-ray scanner – CT (computed tomography)). Note that we are not limited to a particular technology and the system 10 could be an MRI, an ultrasound scanner, a PET scanner, etc.

Process

In reference to the , the present method is implemented by the data processing means 11 of the server 1, and begins with a step (a) of obtaining a kinematic model of said joint before fitting the prosthesis, called the preoperative kinematic model.

By “biomechanical model of a joint”, or “digital twin”, we mean a multidimensional object (in particular two-dimensional or three-dimensional and preferably three-dimensional) articulated, that is to say mobile in the same way as the modeled joint (and comprising all or part of the degrees of freedom of the joint). The model optionally includes deformable parts (corresponding in particular to fat, muscles or ligaments which can be represented by volumetric meshes (for example finite element discretizations), and non-deformable parts (corresponding in particular to bones) which can be represented by 3D surface meshes.

In the context of the present invention, the kinematic model of said articulation can be directly provided to the means 11, but alternatively it is generated.

Step (a) then comprises a sub-step (a1) of obtaining at least one three-dimensional medical image of said joint; and (a2) of constructing said preoperative kinematic model from said three-dimensional medical image of said joint.

Step (a1) may itself comprise the acquisition of said three-dimensional medical image of said joint (and in particular a set of images, preferably representing said joint in a plurality of postures as mentioned above) by the medical imaging device 10.

• Le milieu des épines tibiales, dit centre tibia, noté « TibCenter » ;
• Le centre des deux malléoles, dit centre cheville, noté « AnkleCenter » ;
• L’extrémité antérieure de la tubérosité tibiale antérieure, notée « TTA » ;
• Les fonds des glènes tibiales gauche et droite, notés « TibGlen_L et _R »;
• Le centre hanche noté « HipCenter » ;
• Le centre de l’arche fémorale, dit centre fémur, noté « FemCenter » ;
• l’insertion interne du ligament collatéral médial sur le fémur, noté « FemMCL » ;
• Les insertions des trois fibres (antérieure, postérieure et intermédiaire) du ligament collatéral latéral sur le fémur, notées « FemLCL_A, _P et _I » ;
• L’insertion interne du ligament collatéral médial sur le tibia, noté « TibMCL » ;
• Les insertions des trois fibres (antérieure, postérieure et intermédiaire) du ligament collatéral latéral sur le tibia, notées « TibLCL_A, _P et _I » ;
• Les condyles fémoraux postérieurs du côté droit et gauche notés « LeftPostCond » et « RightPostCond ».

Step (a2) may include the location of notable anatomical points and directions (or "landmarks", see again application FR2300597 on this subject). Typically in the case of the knee it is possible to use all or part of the following points, using any morphological analysis of the bone known to those skilled in the art:

• The middle of the tibial spines, called the tibia center, noted “TibCenter”;
• The center of the two malleoli, called the ankle center, noted “AnkleCenter”;
• The anterior end of the anterior tibial tuberosity, denoted “TTA”;
• The bottoms of the left and right tibial glenoids, denoted “TibGlen_L and _R”;
• The hip center called “HipCenter”;
• The center of the femoral arch, called the femur center, noted “FemCenter”;
• the internal insertion of the medial collateral ligament on the femur, denoted “FemMCL”;
• The insertions of the three fibers (anterior, posterior and intermediate) of the lateral collateral ligament on the femur, denoted “FemLCL_A, _P and _I”;
• The internal insertion of the medial collateral ligament on the tibia, denoted “TibMCL”;
• The insertions of the three fibers (anterior, posterior and intermediate) of the lateral collateral ligament on the tibia, denoted “TibLCL_A, _P and _I”;
• The posterior femoral condyles on the right and left sides denoted “LeftPostCond” and “RightPostCond”.

According to a preferred embodiment, substep (a2) additionally comprises the identification of the bone surfaces of said joint (including the articular surfaces, i.e. the parts of the bone surfaces that are covered by cartilage and that come into contact with another bone to form a joint) in said three-dimensional medical image of said joint. The interest in having these articular and bone surfaces is understood, since it is at their level that the prosthesis will be placed.

To do this, starting from a three-dimensional medical image, we can implement a segmentation process and generate a mesh (made up of facets, in particular triangular ones) representing the external surface of the bones (of which the articular surfaces are the coupled parts). A mesh normalization phase is advantageously implemented in order to eliminate topological artifacts (holes or inconsistencies linked to the connections between the vertices of the mesh) or geometric artifacts (inconsistencies in the orientation of the normals, inversions of the facets or crossings of the edges of the mesh).

Any known technique may be used to construct the model, and in particular the technique defined in application FR2300597 in which the joint kinematics are actually observed via the use of a plurality of medical images associated with a plurality of postures. Alternatively, the kinematics can be simulated and two possible techniques will now be described.

• simulation biomécanique par éléments finis ou
• simulation biomécanique géométrique à partir des formes des surfaces osseuses de ladite articulation identifiées, cette dernière état particulièrement préférée.

The said preoperative kinematic model is thus preferentially constructed by:

• biomechanical simulation by finite elements or
• geometric biomechanical simulation from the shapes of the bone surfaces of said identified joint, the latter being particularly preferred.

Finite element biomechanical simulation is a reference method. It allows simulating an active movement of the joint as it would be produced by a conscious contraction of the muscles of the limb, but it is complex because it uses a digital simulation environment to bring together the anatomical structures studied (bones, ligaments and muscles) within the patient's biomechanical model and to reproduce the boundary conditions that will generate the movement.

It is thus possible to simulate the interactions between non-deformable structures (or "rigid bodies") subjected to forces produced by muscle contractions, and constrained in their movement by the geometry of the patient's articular surfaces and by ligament tensions. Before starting the simulation, the positioning of the ligaments and tendons on the subject studied is carried out by marking anatomical points (the "landmarks" mentioned above). A Hill model (see the document " M. Millard, T. Uchida, A. Seth and SL Delp, “Flexing computational muscle: modeling and simulation of musculotendon dynamics”, Journal of biomechanical engineering, 135 (2), 2013 ") is for example then used to describe the muscle fibers used to produce the movement (quadriceps and its hamstring antagonists for a leg flexion) whose path is based on the landmarks.

The result of the simulation is advantageously a time series of 4x4 rigid transformation matrices, expressed in homogeneous coordinates, giving at each time step, in the case of a flexion/extension movement, the position of the tibia relative to the femur during the movement. Flexion is simulated for example for femur-tibia angles varying from 0° to 85° (measured in the sagittal plane). In addition to these so-called “pose” matrices, finite element analysis also produces numerical value fields (or tensor fields) allowing the quantification of the internal stress state of the biological tissues or mechanical structures (prosthesis) modeled.

Geometric simulation is a clever alternative to biomechanical simulation because it does away with the rheological parameters and complex numerical methods that the latter requires.

Indeed, the geometric approach only considers the shapes of the articular surfaces and formulates hypotheses on the contact between the solids at their point of tangency during the movement. The resulting calculations are therefore several orders of magnitude faster than those required by biomechanical modeling (less than a minute instead of several hours), which makes the geometric approach particularly suitable for an interactive exploration of planning parameters. In addition, this efficiency makes the process compatible with the constraints of implementation in the operating room, and therefore usable during a surgical procedure.

The algorithm for constructing the kinematic model by geometric biomechanical simulation is preferably divided into two parts: a pre-calculation part aimed at defining an anatomical reference from the shapes of the identified bone surfaces of said joint, and a part for calculating the kinematics, which we will now describe for the example of the kinematics of the tibia relative to the femur, and which the person skilled in the art will know how to adapt to any other joint.

Precalculation

1) Construction of the anatomical reference on the tibia noted “TibRef” using the anatomical points identified on the bone, with:

The operator ∏ projects the vector onto a plane whose normal is X _T . At the end of this calculation, TibRef is centered on the middle of the tibial spines, X _T points toward the ankle center and defines the “proximal to distal” direction, Y _T points toward the left of the patient and defines the “right to left” direction, and Z _T points toward the front of the patient and defines the “posterior to anterior” direction. For all the reference frames described here, the naming of the axes and the construction conventions of the reference frame may vary, as long as it is possible to unambiguously and reproducibly attach a 3D reference frame to the modeled bone.

2) Construction of the anatomical reference on the femur noted “FemRef” using the anatomical points identified on the bone, with, similarly to the tibia:

At the end of this calculation, FemRef is centered on the center of the femoral arch, X _F points to the hip center and defines the “distal to proximal” direction, Y _F points to the patient's right and defines the “left to right” direction and Z _F points to the front of the patient and defines the “posterior to anterior” direction.

3) Calculation of the most distal point on the internal condyle of the femur, noted FemDistPt, which is the internal point of contact between the tibia and the femur, knee in extension. This calculation is done in FemRef by looking for the point with the minimum X coordinate and whose Y coordinate is negative (for a right knee) or positive (for a left knee).

4) Extraction of the 2D closed contour corresponding to the intersection between the triangular mesh of the femur (see ) and the plane passing through FemDistPt and whose normal is Y _F . This algorithm is based on an analysis of the shapes of the bone surfaces of said identified joint, in particular here all the facets of the femoral mesh.

5) Extraction of the open subcontour Γ defining the trace of the contact point of the tibia on the femur during flexion. This subcontour is defined as the part of the closed contour extracted in step 3, which: 1) starts at the distal point FemDistPt, 2) reaches the point of minimum coordinate along Z _F , and 3) ends when this contour rises above the plane Z _F = 0.

6) Rectification of Γ to ensure its convexity. The calculation of the knee flexion angle is based on the assumption that Γ is convex in order to guarantee the uniqueness of the contact point for a given flexion angle. The convexity is corrected by projecting all the vertices S of Γ that generate a concavity onto the local convex envelope defined by the segment connecting the vertex preceding S to the vertex following it. This operation is performed iteratively until the contour is stabilized. illustrates this calculation.

8) Each vertex of the contour Γ is then provided with an outgoing normal calculated by finite differences on the discretized contour (see for example points B and C provided with their normals NB and NC on the ). The open contour Γ thus produced carries during the flexion-extension movement a sliding Frenet reference frame noted “FlexRef” which allows us to position the tibia in relation to the femur at each flexion angle, i.e. at each posture.

Calculation of kinematics (relative pose of the tibia in relation to the femur for a given flexion angle)

In reference to the , the part of the algorithm described here allows to calculate for any input flexion angle α, the position of the sliding Frenet frame FlexRef which corresponds, on the contour Γ, to the point of contact between the tibia and the femur.

1) The interval [B, C] containing FlexPt, the origin of the FlexRef reference frame, is defined as the one where the angles between the “proximal to distal” axis and the normals in B and C frame the value of α. The position of FlexPt can be calculated by linear interpolation between these three values.

2) The vector N ("normal") of FlexRef is the linear interpolation between the two normals at the vertices of Γ that frame it. The vector T ("tangential") of FlexRef is orthogonal to N and contained in the sagittal plane, which is the plane also containing Γ. The vector S ("sagittal") of FlexRef (not visible in the because in the vertical plane) is calculated by vector product.

3) The kinematic hypothesis is then as follows: for any angle α, the internal tibial glenoid bottom is in tangential contact in FlexPt with the contour Γ.

4) The tibia is then provided with its own FlexRef reference frame, centered on the bottom of the internal tibial glenoid, and whose axes are oriented in a manner consistent with those of its femoral counterpart (by virtue of the previous kinematic hypothesis).

5) Finally the matrix which positions the tibia relative to the femur in flexion of α degrees is calculated as the following matrix product:

M _TibFem = P _FemRefW XP _{FlexRefFemRef} XP _{TibRefFlexRef} XP _WTibRef , where M _TibFem is the displacement matrix that positions the tibia relative to the femur in the world reference frame denoted “W”; P _FemRefW is a transition matrix that converts the coordinates of the anatomical reference frame FemRef to the world reference frame W; P _{FlexRefFemRef} is the only one of the four transition matrices that depends on α and it allows to pass from the sliding reference frame FlexRef to the anatomical reference frame FemRef; P _{TibRefFlexRef} is the fixed transition matrix that passes from the anatomical reference frame TibRef to the fixed tibial reference frame FlexRef which, during the movement, is superimposed with its mobile counterpart on the femur; finally P _WTibRef is the transition matrix that converts the anatomical coordinates of the patient, expressed in the world reference frame W, to the anatomical reference frame TibRef. The four passage matrices can be easily calculated from the points and vectors defined above.

6) The positioning matrix M _TibFem thus obtained for each flexion angle α can then be used to position the tibial insertions during the movement and calculate the values of any set of functional metrics such as the variations in the lengths of the collateral ligaments (anisometries), or the constraints within these ligaments (calculated by means of a finite element model coupled to the geometric model, for example).

Indeed, step (a) preferably includes in a sub-step (a3) the estimation of the preoperative values (i.e. as is, before fitting the prosthesis) of a set of functional metrics of said joint based on said preoperative kinematic model.

A functional metric set is a group of one or more biomechanical metrics (the set may contain a single functional metric, although it is usually a plurality) that functionally describe an aspect of the joint.

Some functional metrics are called "morphological" in that they allow the shape of a bone to be characterized before and after prosthesis placement in order to quantify the geometric gap between the native (preoperative) and prosthetic (postoperative) articular surfaces. Morphological metrics can thus consider differences in distance between the two surfaces or differences in volume by comparing the volume of the bone removed with the volume of the prosthesis that was substituted for it. It is understood that these are indeed functional metrics because the morphology of the joints constrains their function.

According to a preferred embodiment, in particular in the case of the knee, said set of functional metrics defines a ligament balance of said joint, the set of functional metrics being in particular the set of variation profiles of the lengths of the ligaments of said joint, called anisometries. The ligament balance in fact represents the “balance” in the bilateral tension of the ligaments, and must be disturbed as little as possible by the fitting of the prosthesis.

According to a preferred embodiment, said set of functional metrics defines trajectories of the joint such as the patellar stroke, and said set is then the values of the 6 degrees of freedom (3 Euler rotations and 3 translations) at any time of the movement. Another way to define these successive poses is to choose 3 points (non-aligned) on the surface of the bone model (triangular) and compare at any time the position of these 3 points on the “target” bone with the position of these same 3 points on the bone whose trajectory is being optimized. A third way consists of not restricting oneself to 3 points but on the contrary considering all the points of the mesh as reference points. The optimization of the trajectory will then consist of finding the pose of the prosthesis allowing to approach as best as possible, at each moment, the positions of all the points of the target mesh at the moment considered.

Other sets of functional metrics can be chosen, in particular depending on the risks and objectives of the prosthesis fitting. Several sets of functional metrics can even be chosen and combined, for example with the measurement at each instant of the rate of elongation of ligament fibres, or the measurement at each instant of internal constraints within tissues whose exposure to excessive internal forces is to be limited. In general: any quantity reflecting a degree of adequacy or inadequacy between the current state of the model and a functional objective can be used. The inadequacy measures should then be minimised while the adequacy measures will be maximise.

In all cases, the preoperative values of functional metrics can be easily read on the preoperative model, and are preferentially used as "target" values, i.e. values to be approached as closely as possible in the postoperative state (which would indicate an absence of excessive disturbance of the surrounding soft tissues of the knee between before and after surgery). Alternatively, one may wish to improve an existing situation (if for example the joint presents a pathology) via the fitting of the prosthesis, and therefore one has values calculated from the preoperative values, but different from the latter, or even have predetermined target values and avoid this step of estimating preoperative values. Alternatively, they can still be measured on the patient using ancillaries or 3D tracking devices.

Postoperative prediction

The idea behind the present invention is, instead of trying to directly determine optimal values of the prosthesis fitting parameters, which proves impossible in practice, to proceed by iterations and to converge towards these optimal values (within a clinically admissible set of values).

In this respect, in a step (b), the means 11 construct a kinematic model of said joint after fitting of the prosthesis, called a postoperative kinematic model, for current values of the fitting parameters of said prosthesis, by modifying said preoperative kinematic model. To reformulate, the fitting of the prosthesis will be simulated using said preoperative kinematic model. To do this, it is possible to simply implement a substitution of a portion of the bone surface of the preoperative model by a volume representing the prosthesis, in a manner determined by said fitting parameters, as can be seen for example in the . The so-called "current" values are intended to initialize the procedure and are typically either default values or candidate values proposed by the surgeon, potentially already close to the optimal values, which shortens the procedure, but they could quite be arbitrary values.

Step (b) can thus involve a new traditional biomechanical modeling, for example by finite elements, or, advantageously, use geometric modeling whose principles have been described above and which is immediately transposed to the post-operative state, by simply replacing the patient's pre-operative articular surfaces with the prosthetic articular surfaces. To reformulate, "modified" bone surfaces of said joint are determined for the current values of the fitting parameters of said prosthesis, corresponding to the bone surfaces equipped with the prosthesis. Said post-operative kinematic model is then constructed by new geometric biomechanical simulation from the shapes of the modified bone surfaces. It is understood that a new complete kinematic model is constructed (possibly reusing all or part of the precalculations of the relative displacements between the modeled bone, tissue and/or prosthetic entities), but since the geometric biomechanical simulation is very fast, there is no problem in repeating it completely on the basis of the modified bone surfaces.

Then, in a step (c), we predict postoperative values of said set of functional metrics of said joint based on said postoperative kinematic model. This step is typically implemented in the same way as the possible step (a3) of estimating the preoperative values of said set of functional metrics of said joint based on said preoperative kinematic model, the difference being that we work on the modified model which includes the prosthesis.

This step is referred to as a prediction since the postoperative kinematic model remains theoretical, even if so-called validation and verification techniques allow the models used to be calibrated and certified in order to guarantee high reliability in the representation of the modeled structures.

Then, in a step (d), the means 11 validate or not the current values of the fitting parameters of said prosthesis according to said predicted postoperative values of the set of functional metrics. The idea is that the current values of the fitting parameters are acceptable if the postoperative values of the metrics are themselves acceptable.

Typically, step (d) compares the predicted postoperative values of the functional metric set and the target values, in particular said preoperative values or predefined values.

For this measurement of the deviation between the current values and the target values, any mathematically relevant criterion can be used, for example an error rate, a maximum quadratic distance, etc. A preferred embodiment will be seen later.

If the current values of the fitting parameters of said prosthesis are validated (for example because the predicted postoperative values of the set of functional metrics are sufficiently close to the target values), then the method can stop. The method can for example comprise a step (f) of using the validated values of the fitting parameters, in a medical application (for example passive surgical navigation or robotic performance of the surgical procedure). Step (f) can comprise for example the display of said validated current values on the interface 13, intended for the surgeon, who then knows that he can apply them, and/or the sending of the parameters to means of generating the prosthesis (for example a 3D printer, machining equipment, etc.) on the basis of the parameters.

Step (f) may also include the actual placement of the prosthesis on the patient, during a surgical operation.

Otherwise, if the current values of the fitting parameters of said prosthesis are not validated, the method comprises a step (e) of modifying the current values of the fitting parameters of said prosthesis (where appropriate with the possibility of locking certain parameters, either because their current value is the one that is desirable, or because it is not desired for the algorithm to propose values outside a range of predetermined acceptable values), of updating the postoperative kinematic model, then of repeating steps (c) and (d) on the basis of the updated postoperative kinematic model.

In other words, step (b) is repeated not on the basis of the preoperative model, but on the basis of the “unvalidated” postoperative model, on the basis of new parameters, and steps (c) and (d) are repeated until values of the pose parameters are found which are validated (and step (f) is implemented).

To achieve “optimal” pose parameters, one can implement any known optimization algorithm: gradient descent, stochastic methods, genetic algorithms, etc. One could even, naively, randomly test new values of the pose parameters.

According to a particularly preferred embodiment, the current values of the fitting parameters of said prosthesis are validated when they minimize a cost function comparing the predicted postoperative values and the target values of the set of functional metrics.

This allows that the current values of the pose parameters of said prosthesis can be modified in step (e) by a gradient descent algorithm on said cost function, which guarantees convergent behavior.

For example, in the case where said set of functional metrics defines a ligament balance, said cost function is advantageously the sum over all the ligaments of said joint of the quadratic deviations between the predicted postoperative values and the target values of the anisometries, and in particular, in the case of the knee, in accordance with the formula: , where P ₁ ,…,P _N denote the pose parameters, L=1,2,3 or 4 denotes the four free collateral ligaments, α an index that denotes the posture (or directly a flexion angle – typically from 0° to 70°), L _Pre (L,α) the preoperative length of ligament L at posture α and L _Post (P ₁ …P _N ,L,α) the corresponding postoperative length for pose parameters P ₁ ,…,P _N .

Note that in the implementation example given here, to arrive at four collateral ligaments of the knee, in practice the lateral collateral ligament (LCL) is represented by a single fiber, while the medial collateral ligament (MCL) is divided into three fibers, anterior (aMCL), intermediate (iMCL) and posterior (pMCL), which present distinct anisometric tendencies.

Alternatively, in the case where said set of functional metrics defines the patellar kinematics, said cost function can be the quadratic sum of the deviations between the predicted postoperative degrees of freedom (spatial translations and rotations) and the target values of these degrees of freedom. Another possible formulation could be based on the calculation of a Hausdorff distance (symmetric or not) between a 3D surface model of the patella in its predicted postoperative pose and the same model in the target postoperative pose.

Results

Figures 5a–5d demonstrate the effectiveness of the present method on an example of PTG placement. The qualitative comparison consists of validating the lengthening or shortening trends of the four aforementioned collateral ligament fibers (LCL, aMCL, iMCL, and pMCL) in order to validate that the model predicts a consistent trend.

There and the first represent the estimated preoperative anisometries for an example of a joint when said preoperative kinematic model is respectively constructed by finite element biomechanical simulation and by geometric biomechanical simulation, expressed as a function of the angle α as a percentage of elongation relative to the reference length of the ligament (when the knee is in extension, i.e. α=0°).

The results of the two models are not identical but show exactly the same trends of lengthening or shortening.

Based on the preoperative kinematic model constructed by geometric biomechanical simulation (that of the ) we first implemented the first iteration of the postoperative kinematic model construction, i.e. step (b), based on initial values of the prosthesis fitting parameters, provided by an expert operator, as current values, and the prediction of the corresponding postoperative values of the anisomers (first occurrence of step (c)). The result, visible on the , shows initially unphysiological anisometric tendencies (large deviations from the ), so that these current values are not validated (step (d)).

According to step (e), the current values of the fitting parameters of said prosthesis are optimized, the postoperative kinematic model is updated, and steps (c) and (d) are repeated on the basis of the updated postoperative kinematic model.

After a few iterations, we clearly see an evolution of the anisometric trends which, at the end of the optimization, are very close to the natural anisometries of the knee, see the (compare with the ). The residual error is 2.51 mm on average over the four insertion points and over the entire range of motion. This residual is mainly due to the mechanical design of the prosthesis and is therefore difficult to reduce.

In terms of performance, the pre-calculations required to build the pre- and post-operative kinematic models take about 2 seconds. The pre- or post-operative knee kinematics can then be simulated in 1.5 milliseconds. A gradient descent optimization of 2000 iterations results in optimal values of the pose parameters where the average deviation on the position of the tibial insertions over the entire flexion-extension movement is 2.51 mm as explained before). With a geometric biomechanical model this calculation requires the evaluation of the anisometries for about 20,000 sets of current values of the pose parameters (in order to calculate the gradient by finite differences at each step) but takes only 30 seconds.

Server

According to a second aspect, the invention relates to the server 1 for implementing the method according to the first aspect.

Thus, this server 1 comprises, as explained, at least data processing means 11 and a memory 12. The server may further comprise an interface 13 such as a screen. This is typically a server for determining parameters for fitting a prosthesis to a patient's joint.

• Obtenir un modèle cinématique de ladite articulation avant pose de la prothèse, dit modèle cinématique préopératoire ;
• Construire un modèle cinématique de ladite articulation après pose de la prothèse, dit modèle cinématique postopératoire, pour des valeurs courantes des paramètres de pose de ladite prothèse, en modifiant ledit modèle cinématique préopératoire ;
• Prédire des valeurs postopératoires d’un ensemble de métriques fonctionnelles de ladite articulation en fonction dudit modèle cinématique postopératoire ;
• Valider ou non les valeurs courantes des paramètres de pose de ladite prothèse en fonction desdites valeurs postopératoires prédites de l’ensemble de métriques fonctionnelles ;
• Si les valeurs courantes des paramètres de pose de ladite prothèse ne sont pas validées, modifier les valeurs courantes des paramètres de pose de ladite prothèse, mettre à jour le modèle cinématique postopératoire, puis répéter les étapes consistant à mettre à jour le modèle cinématique postopératoire, puis répéter les étapes consistant à prédire les valeurs postopératoires d’un ensemble de métriques fonctionnelles de ladite articulation, et valider ou non les valeurs courantes des paramètres de pose de ladite prothèse, sur la base du modèle cinématique postopératoire mis à jour

The data processing means 11 are configured to implement steps consisting of:

• Obtain a kinematic model of said joint before fitting the prosthesis, called a preoperative kinematic model;
• Construct a kinematic model of said joint after fitting of the prosthesis, called postoperative kinematic model, for current values of the fitting parameters of said prosthesis, by modifying said preoperative kinematic model;
• Predicting postoperative values of a set of functional metrics of said joint based on said postoperative kinematic model;
• Validate or not the current values of the fitting parameters of said prosthesis based on said predicted postoperative values of the set of functional metrics;
• If the current values of the pose parameters of said prosthesis are not validated, modifying the current values of the pose parameters of said prosthesis, updating the postoperative kinematic model, then repeating the steps of updating the postoperative kinematic model, then repeating the steps of predicting the postoperative values of a set of functional metrics of said joint, and validating or not the current values of the pose parameters of said prosthesis, on the basis of the updated postoperative kinematic model

According to a third aspect, the invention proposes a system comprising said server 1, as well as a connected medical imaging device 10 (via the network 20).

• Obtenir depuis ledit dispositif d’imagerie médicale 10 au moins une image médicale tridimensionnelle de ladite articulation ;
• Construire ledit modèle cinématique préopératoire à partir de ladite image médicale tridimensionnelle de ladite articulation.

The data processing means 11 are then further configured to:

• Obtain from said medical imaging device 10 at least one three-dimensional medical image of said joint;
• Construct said preoperative kinematic model from said three-dimensional medical image of said joint.

• Estimer des valeurs préopératoires dudit ensemble de métriques fonctionnelles de ladite articulation en fonction dudit modèle cinématique préopératoire ; ou encore
• utiliser les valeurs des paramètres de pose validées, par exemple pour fabriquer la prothèse par impression 3D.

The data processing means 11 can also be configured to:

• Estimate preoperative values of said set of functional metrics of said joint based on said preoperative kinematic model; or
• use the validated pose parameter values, for example to manufacture the prosthesis by 3D printing.

Computer program product

According to a fourth and a fifth aspect, the invention relates to a computer program product comprising code instructions for the execution (on the data processing means 11 of the server 1) of a method according to the first aspect of determining parameters for fitting a prosthesis to a patient's joint, as well as storage means readable by computer equipment (for example the data storage means 12 of the server 1) on which this computer program product is found.

Claims (15)

Method for determining parameters for fitting a prosthesis to a patient's joint, the method being characterized in that it comprises the implementation by data processing means (11) of a server (1) of steps of:

1. Obtaining a kinematic model of said joint before fitting the prosthesis, called a preoperative kinematic model;
2. Construction of a kinematic model of said joint after fitting of the prosthesis, called postoperative kinematic model, for current values of the fitting parameters of said prosthesis, by modifying said preoperative kinematic model;
3. Prediction of postoperative values of a set of functional metrics of said joint based on said postoperative kinematic model;
4. Validation or not of the current values of the fitting parameters of said prosthesis according to said predicted postoperative values of the set of functional metrics;
5. If the current values of the fitting parameters of said prosthesis are not validated, modification of the current values of the fitting parameters of said prosthesis, updating of the postoperative kinematic model, then repetition of steps (c) and (d) on the basis of the updated postoperative kinematic model.

The method of claim 1, wherein step (a) comprises a substep (a1) of obtaining at least one three-dimensional medical image of said joint; and (a2) of constructing said preoperative kinematic model from said three-dimensional medical image of said joint. The method of claim 2, wherein substep (a2) comprises identifying the bony surfaces of said joint in said three-dimensional medical image of said joint. The method of claim 3, wherein said preoperative kinematic model is constructed by finite element biomechanical simulation or by geometric biomechanical simulation from the shapes of the bone surfaces of said identified joint. Method according to claim 4, wherein said preoperative kinematic model is constructed by geometric biomechanical simulation from the shapes of the bone surfaces of said identified joint, step (b) comprising modifying the shapes of the bone surfaces of said joint, for the current values of the fitting parameters of said prosthesis, and constructing said postoperative kinematic model by geometric biomechanical simulation from the modified shapes of the bone surfaces. Method according to one of claims 2 to 5, in which step (a1) comprises the acquisition of said three-dimensional medical image of said joint by a medical imaging device (10). The method of one of claims 1 to 6, wherein step (d) compares the predicted postoperative values of the set of functional metrics and the target values of the set of functional metrics. Method according to claim 7, wherein step (a) comprises a sub-step (a3) of estimating the preoperative values of said set of functional metrics of said joint as a function of said preoperative kinematic model, said target values being the estimated preoperative values. Method according to one of claims 7 and 8, in which the current values of the fitting parameters of said prosthesis are validated when they minimize a cost function comparing the predicted postoperative values and the target values of the set of functional metrics, the current values of the fitting parameters of said prosthesis being modified in step (e) by a gradient descent type algorithm on said cost function. Method according to one of claims 1 to 9, in which said set of functional metrics defines a ligament balance of said joint, the functional metrics being in particular profiles of variation of the lengths of the ligaments of said joint, called anisometries. A method according to claims 7 and 8 in combination, wherein said cost function is the sum over all ligaments of said joint of the quadratic deviations between the predicted postoperative values and the target values of the anisometries. Server (1) for determining parameters for fitting a prosthesis to a patient's joint, characterized in that it comprises data processing means (11) configured to:

• Obtain a kinematic model of said joint before fitting the prosthesis, called a preoperative kinematic model;
• Construct a kinematic model of said joint after fitting the prosthesis, called a postoperative kinematic model, for current values of the fitting parameters of said prosthesis, by modifying said preoperative kinematic model;
• Predicting postoperative values of a set of functional metrics of said joint based on said postoperative kinematic model;
• Validate or not the current values of the fitting parameters of said prosthesis based on said predicted postoperative values of the set of functional metrics;
• If the current values of the pose parameters of said prosthesis are not validated, modifying the current values of the pose parameters of said prosthesis, updating the postoperative kinematic model, then repeating the steps of predicting the postoperative values of a set of functional metrics of said joint, and validating or not the current values of the pose parameters of said prosthesis, on the basis of the updated postoperative kinematic model.

System comprising a server (1) according to claim 12 and a medical imaging device (10), the data processing means (11) being further configured to:

• Obtaining from said medical imaging device (10) at least one three-dimensional medical image of said joint;
• Construct said preoperative kinematic model from said three-dimensional medical image of said joint.

Computer program product comprising code instructions for executing a method according to one of claims 1 to 12 for determining parameters for fitting a prosthesis to a patient's joint, when said program is executed on a computer. Storage medium readable by computer equipment on which is recorded a computer program product comprising code instructions for executing a method according to one of claims 1 to 12 for determining parameters for fitting a prosthesis to a patient's joint.