Method for modelling a joint of a patient

Abstract

The present invention relates to a method for modelling a joint of a patient, the method comprising carrying out the steps of: (a) obtaining a candidate biomechanical model of the joint and a first set of medical images of the joint, representing the joint in a posture; (b) for at least one medical image of the first set, implementing at least one simulation of the candidate biomechanical model in which the joint has the same posture as in the medical image; (c) constructing an error model of the candidate biomechanical model by comparing, for at least one biomechanical metric of the joint and for at least one medical image of the first set for which at least one simulation has been implemented, the values of the biomechanical metric in the medical image and in the simulation(s); (d) validation or non-validation of the candidate biomechanical model on the basis of the error model.

Description

[0001] DESCRIPTION

[0002] Title: Method for modeling a patient's joint

[0003] GENERAL TECHNICAL FIELD

[0004] The present invention relates to the field of biomechanics. More specifically, it relates to a method for modeling a patient's joint for orthopedic applications.

[0005] STATE OF THE ART

[0006] Before an intervention (particularly surgical) on a joint such as the knee, it is known to generate a biomechanical model of the joint, called a "digital twin", in order to help the practitioner plan this intervention and optimize the therapeutic strategy. More precisely, the digital twin allows not only the functional evaluation of the joint, but also the personalization of prostheses / orthoses, or the guidance of the surgical procedure.

[0007] The digital twin is reconstructed from 2D or 3D medical images of the joint, adapted to the problem to be treated.

[0008] The difficulty is that known techniques do not guarantee the accuracy of the digital twin (i.e. that it faithfully represents reality), and we are forced to perform manual validation by an expert, by comparing metrics of interest measured on the subject to the corresponding metrics predicted by the model, see for example the document Validation of computational models in biomechanics; HB Henninger 1, SP Reese, AE Anderson, JA Weiss.

[0009] These manual validation procedures are complex, time-consuming, and error-prone, even when performed by an experienced practitioner. It is also known that medical data processing exhibits high inter-operator variability, which undermines the objectivity sought by a validation procedure. There is therefore a need for an automatic and reliable procedure for validating a digital twin of a joint that is efficient, objective, and versatile.

[0010] The invention improves the situation.

[0011] PRESENTATION OF THE INVENTION

[0012] The present invention therefore relates, according to a first aspect, to a method for modeling a patient's joint, the method being characterized in that it comprises the implementation, by data processing means of a server, of steps of:

[0013] (a) Obtaining a candidate biomechanical model of said joint and a first set of medical images of said joint, representing said joint in a posture of a first set of postures, called validation images;

[0014] (b) For at least one medical image of said first set of medical images of said joint, implementing at least one simulation of the candidate biomechanical model in which said joint has the same posture as in said medical image of said first set of images;

[0015] (c) Building an error model of the candidate biomechanical model by comparing, for at least one biomechanical metric of said joint and for at least one medical image of said first set of medical images of said joint for which at least one simulation has been implemented, the values ​​of said biomechanical metric in said medical image and in the simulation(s) implemented for said medical image;

[0016] (d) Validation or not of the candidate biomechanical model depending on the error model.

[0017] According to advantageous and non-limiting characteristics: Which step (a) comprises sub-steps (a1) of obtaining said first set of medical images of said joint, as well as a second set of medical images of said joint, representing said joint in a posture of a second set of postures; and (a2) of generating said candidate biomechanical model from the second set of medical images.

[0018] The first set of postures and the second set of postures are distinct.

[0019] Step (a1) also comprises obtaining a third set of medical images of said joint, representing said joint in a posture of a third set of postures; step (a) comprising a sub-step (a3) ​​of calibrating the candidate biomechanical model as a function of said third set of medical images.

[0020] The first set of postures and the third set of postures are distinct; and the second set of postures and the third set of postures are different but not necessarily distinct.

[0021] Step (a1) comprises the acquisition of the second set of medical images, and where appropriate of the third set of medical images, by a medical imaging device.

[0022] Step (d) comprises calculating, for the biomechanical metric(s) and the medical image(s) of the first set, a confidence interval on the value of said biomechanical metric from the error model, and the candidate biomechanical model is not validated if a width of at least a given number of the calculated confidence intervals exceeds an uncertainty threshold of the metric.

[0023] The values ​​of said biomechanical metric in said medical image and in the simulation(s) implemented for said medical image are calculated in step (c) as a function of the positions of characteristic anatomical points of said joint in said medical image and in the simulation(s) implemented for said medical image. There is a plurality of characteristic anatomical points of said joint, and said biomechanical metric is a distance between two of said characteristic anatomical points of said joint or an angle defined by three of said characteristic anatomical points of said joint.

[0024] The method comprises a step (e) of revising the candidate biomechanical model if it is not validated, and then repeating at least steps (b) to (d) based on the revised biomechanical model as a new candidate biomechanical model.

[0025] The method comprises a step (f) of using the validated biomechanical model, comprising implementing at least one simulation of the validated biomechanical model in which said joint has a target posture.

[0026] Step (f) comprises using said error model to assess a level of uncertainty in the result of said simulation of the validated biomechanical model.

[0027] Either said candidate biomechanical model is non-deterministic, and in step (b) for each medical image of said first set a plurality of simulations is implemented; or said candidate biomechanical model is deterministic, and in step (b) for each medical image of said first set a single simulation is implemented.

[0028] According to a second aspect, the invention relates to a server for modeling a patient's joint, characterized in that it comprises data processing means configured to:

[0029] - Obtaining a candidate biomechanical model of said joint as well as a first set of medical images of said joint, representing said joint in a posture of a first set of postures, called validation images;

[0030] - For at least one medical image of said first set of medical images of said joint, implementing at least one simulation of the candidate biomechanical model in which said joint has the same posture as in said medical image of said first set of images;

[0031] - Constructing an error model of the candidate biomechanical model by comparing, for at least one biomechanical metric of said joint and for at least one medical image of said first set of medical images of said joint for which at least one simulation has been implemented, the values ​​of said biomechanical metric in said medical image and in the simulation(s) implemented for said medical image;

[0032] - Validate or not the candidate biomechanical model depending on the error model.

[0033] 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:

[0034] - Obtaining from said medical imaging device said first set of medical images of said joint, as well as a second set of medical images of said joint, representing said joint in a posture of a second set of postures;

[0035] - generate said candidate biomechanical model from the second set of medical images.

[0036] 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 modeling 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 modeling a joint of a patient. PRESENTATION OF THE FIGURES

[0037] Other characteristics and advantages of the present invention will appear on reading the following description of a preferred embodiment. This description will be given with reference to the appended drawings in which:

[0038] [Fig. 1] Figure 1 is a diagram of a system for implementing the method according to the invention;

[0039] [Fig. 2] Figure 2 is a flowchart illustrating the steps of an embodiment of the method according to the invention;

[0040] [Fig. 3] Figure 3 illustrates the sets of postures used in one embodiment of the method according to the invention;

[0041] [Fig.4a] Figure 4a schematically represents a first geometric model for calculating uncertainty intervals on a first example of biomechanical metric;

[0042] [Fig.4b] Figure 4b schematically represents a second geometric model for calculating uncertainty intervals on a second example of biomechanical metric.

[0043] DETAILED DESCRIPTION

[0044] Architecture

[0045] The present invention relates to a method for modeling a patient's joint in a system represented in Figure 1. The joint, or articulation, is an anatomical element of the patient's body forming a junction zone between bone ends and forming at least one degree of freedom. Said joint 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 joint can take a posture (or pose) from among a plurality of possible postures (mathematically, Pau denotes the set of possible postures, see below), typically defined by one or more parameters such as angles, each corresponding to a possible movement of the joint. For example, the knee can thus produce the following movements:

[0046] - Extension / flexion of the leg on the thigh (approximately 160° range);

[0047] - Internal / external rotation of the leg on the thigh (approximately 20° range of motion with the knee bent);

[0048] - Antero-posterior translation of the tibial plateau (approximately 10 mm).

[0049] The modeling of a joint requires in particular at least the validation of a biomechanical model of said joint (i.e. the evaluation of the capacity of the model to represent all or part of a real system in a predefined precision corridor - here the patient's joint), the process requiring the prior generation of said model (or a model to be validated is provided). It is understood that the biomechanical model is in fact personalized, that is to say that it is specifically adapted to this joint of this patient, and that the validation is for this joint and not another. A "global" model, i.e. which would be transposable to all patients, cannot in fact be sufficiently precise (and would therefore not be validated by the present process).

[0050] For convenience, we speak of a “candidate” biomechanical model before validation, then of a “validated” biomechanical model for said patient joint if the validation is successful, i.e. the candidate biomechanical model is not rejected. In a preferred embodiment, the rejected model can be “revised” and a new candidate model is obtained which will itself be subject to validation, etc.

[0051] Thus, the output of the process is generally a validated biomechanical model, but in some cases it may be information that a satisfactory biomechanical model has not been obtained (if the process does not provide for revision or if this proves impossible, see below).

[0052] In all cases, by "biomechanical model of a joint", or "digital twin" as explained, 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 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.

[0053] The model is further advantageously defined by:

[0054] - Input variables, in particular those called "boundary conditions" which allow to define a posture (for example the angles of extension / flexion and internal / external rotation for the knee; the activation level of a muscle, etc.). Mathematically, we define as biomechanical modeling space the space parameterized by said input variables, and the number of input variables defines the dimension of said space (for example in a 1-dimensional model we have just the flexion angle as input variable, and in a 2-dimensional model we have the flexion angle and the rotation angle);

[0055] - Configuration parameters: o Constitutive laws: mechanical laws that govern the mechanical response of tissues to external stresses. Several types of laws can be considered depending on their relevance (targeted precision, realism, etc.); o Biomechanical parameters: coefficients of elasticity, Poisson, friction, damping, etc. The values ​​of these parameters can be deterministic (constant) or stochastic (variable, defined by a probability law);

[0056] - Output data, in particular a deformed configuration of the model ("the deformed"), constituting a simulation of said joint for said input variables, on which one can obtain the positions of anatomical points characteristic of said joint (also called anatomical points of interest, or more simply "landmarks") which can be associated with the non-deformable parts as well as with the deformable parts (points, curves, etc.), and the values ​​of biomechanical metrics linked to said positions of the landmarks.

[0057] The characteristic anatomical points can be, for example, in the case of the knee:

[0058] - “Bony” anatomical points such as o H (hip): hip center (center of the femoral head); o A (ankle): ankle center (middle of the 2 malleoli); o K (knee): knee center, also called femur center (central point of the femoral arch); o T (tibia): tibia center

[0059] - Anatomical points “bone tissue / soft tissue interface” such as o insertions of the collateral ligaments (internal and external); o femoral and tibial insertions of the anterior and posterior cruciate ligaments.

[0060] The present invention will not be limited to any characteristic anatomical point, any metric and generally any type of biomechanical model of a joint. Furthermore, different models may be used for different joints.

[0061] 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.).

[0062] Preferably, a medical imaging system 10 is also applied for acquiring medical images of said joint.

[0063] 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 for the system 10 (to control it and obtain the acquired medical images).

[0064] Said medical images are typically 3D volumetric images, possibly reconstructed from 2D sections, i.e. tomographies 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, a PET scanner, etc.

[0065] Process

[0066] With reference to Figure 2, the present method is implemented by the data processing means 11 of the server 1, and begins with a step (a) of obtaining a candidate biomechanical model of said joint and at least a first set (denoted E1) of medical images of said joint, called validation images. These images will make it possible to validate or not the candidate biomechanical model. O

[0067] As will be seen, it is also advantageous to obtain a second set (denoted E2) of medical images of said joint, called initialization images, and where appropriate a third set (denoted E3) of medical images of said joint, called calibration images. These images are used to generate said candidate biomechanical model, but alternatively the method can be used to validate a model provided as is, and then only the first set is required. In all cases, all the images are naturally all of the same joint of the same patient.

[0068] Each image in each of these sets represents the said joint in a posture, as explained before. To rephrase, a medical image is a snapshot of the joint in which it presents a particular posture among the set of possible postures, and thus each medical image is "associated" with the corresponding posture. Preferably all medical images are associated with different postures, even if there may be some duplicates, and mathematically:

[0069] - Let us have a discrete set of Np postures for which a medical image has been acquired (noted Pacq, with Pacq <= Pan, this last theoretical set encompassing all the postures that can be adopted by the joint of interest), and we can note h the medical image associated with the i-th posture, with 1 <i<Np.

[0070] - Either the posture is defined by one or more parameters with variable value (a flexion angle for example) and we can directly note l(xi...xd) the medical image associated with the posture in which the parameters have the value xi ...Xd. P a ii is then the set of possible values ​​of the vector [xi...xd].

[0071] In all cases we can define a first set of postures (noted P1, with P1 c Pacq) as the set of postures associated with the medical images of the first set of medical images (validation images), and where appropriate, respectively, a second / third set of postures (noted P2 / P3, with P2 / P3 <= P acq) as the set of postures associated with the medical images of the second / third set of medical images (initialization / calibration images). Conversely, each image of the first set of medical images E1 represents said joint in a posture of the first set of postures P1, and where appropriate each image of the second / third set of medical images E2 / E3 represents said joint in a posture of the second / third set of postures P2 / P3.

[0072] Preferably:

[0073] - the first set of postures and the second set of postures are distinct (without intersection), ie P1 Cl P2 = 0, which means that there is no validation image representing the joint in the same posture as an initialization image; - the first set of postures and the third set of postures are distinct (without intersection), ie P1 Cl P3 = 0, which means that there is no validation image representing the joint in the same posture as a calibration image;

[0074] - the second set of postures and the third set of postures are different (not identical) but not necessarily distinct (ie there may be a common posture, and therefore the same medical image in the second and third sets of medical images) and even we may have P2 included in P3, as long as aPeP3 such as P0P2.

[0075] Indeed, we understand that, for validation to be as reliable as possible, images on the basis of which the candidate model was generated should not be reused as validation images.

[0076] This is illustrated by Figure 3: we see that the sets P1, P2 and P3 are all included in the Pacq set of postures for which an image was acquired, itself included in the Pau set of possible postures, with the validation set P1 distinct from the initialization and calibration sets P2, P3. The sets P1, P2 and P3 can also be as diverse as possible in the said Pacq set, and in particular the first set P1. It is indeed desirable that the validation images in particular constitute a representative sample of the modeling space.

[0077] Preferably, step (a) comprises sub-steps (a1) of obtaining (preferably by acquisition, by the medical imaging device 10), said first, second and / or third set(s) of medical images of said joint; (a2) of generating said candidate biomechanical model from said second set of medical images; and advantageously (a3) ​​of calibrating the candidate biomechanical model as a function of said third set of medical images.

[0078] Typically, step (a1) consists of: - acquiring a large number of medical images (the set of acquired images being noted E aC q, and we recall that Pacq is the set of postures associated with the medical images of this last set E acq ) corresponding to varied postures, in particular by asking the patient to move his joint, if possible over the full range of motion (for example complete flexion / twisting of the knee),

[0079] - then select, in this set E acq , E1, E2 and / or E3, for example simply by partitioning E acq , or by first selecting, from the set P acq postures, the sets P1, P2 and / or P3 by diversifying as much as possible, then by constructing E1, E2 and / or E3 respectively as the sets of medical images associated with the postures of sets P1, P2 and / or P3.

[0080] Steps (a2) and, if applicable, (a3) ​​aim to obtain the said candidate biomechanical model. Step (a2) may be sufficient, but step (a3) ​​allows the generated model to be improved before using it.

[0081] The said calibration can be seen as a "fine-tuning" of a "provisional" model, in particular to refine certain parameters of the model, so as to significantly increase the chances of it being validated.

[0082] Any technique known to those skilled in the art may be used for steps (a2) and, where appropriate, (a3), see for example the documents Towards Automatic Generation of Patient-Specific Knee Models, Elaheh Elyasi, Marek Bucki, Boubaker Asaadi, Daniel Elizondo and Antoine Perrier, in Proceedings of The 20th Annual Meeting of the International Society for Computer Assisted Orthopaedic Surgery, vol. 5, pp. 66-68, 2022, or A fast and robust patient specific Finite Element mesh registration technique: application to 60 clinical cases, Marek Bucki, Claudio Lobos, Yohan Payan, in Medical Image Analysis, vol. 3, pp. 303—17, 2010.

[0083] We will now be able to verify that the configurations produced at the output of the candidate model coincide with at least one validation image (and preferably a large number of the images in the first set or even all of them).

[0084] To do this, in a main step (b), the data processing means 11 implement at least one simulation of the candidate biomechanical model in which said joint has the same posture as in said medical image of said first set of validation images E1. Two embodiments will be distinguished: a non-deterministic mode in which there are several simulations, and a deterministic mode in which a single simulation is sufficient, which will be detailed later.

[0085] Generally speaking, by simulation, we mean putting the model in a state so as to imitate the validation image. More precisely, said simulation reproduces the posture in which the joint is represented in said validation image, by applying the values ​​of adapted input variables, that is to say by defining boundary conditions of the model. Indeed, we recall that each medical image is a snapshot of the joint in a particular posture, while the model presents input variables and theoretically allows reproducing any posture from the set of possible Pau postures (and therefore from the Pacq set it contains).

[0086] Then, in a following step (c), for at least one biomechanical metric of said joint (preferably for each) and for at least one validation image for which at least one simulation has been implemented (preferably for each validation image for which one or more simulations have been implemented), an error model of the candidate biomechanical model is constructed (for this joint of this patient) as a function of the values ​​of the biomechanical metric(s) in said validation image and in the simulation(s) implemented for this validation image.It is recalled that said biomechanical metrics are typically linked to positions of characteristic anatomical points (called "landmarks"), in particular either directly the positions of the anatomical points in a given reference frame, or quantities calculated from these positions of characteristic anatomical points, in particular distances between two anatomical points or angles defined by three anatomical points, but other quantities such as volumes can be used.

[0087] For example:

[0088] - in the case of bony anatomical points, the HKA angle (Hip - Knee - Ankle) can be taken as a metric in the frontal (radiological) plane, or in the sagittal plane, or even in 3D space;

[0089] - in the case of anatomical points of bone tissue / self tissue interface, we can take as metric the elongation distance (between the insertion points) of the collateral ligaments, or the cruciate ligaments, as a function of the flexion angle

[0090] - By choosing the appropriate anatomical points (points at the end of the bones), we can take as metric the length / width of the bones, the diameter of the femoral head, etc.

[0091] In all cases, typically:

[0092] - if the biomechanical metrics are the positions of the anatomical points, their values ​​are directly simulated;

[0093] - if the biomechanical metrics are the distances / angles between positions of anatomical points or others, their values ​​are calculated from the simulated values ​​of the positions of the anatomical points.

[0094] The principle of validation consists of calculating predictions using the candidate model and using the images as ground truth to assess the accuracy of said predictions. We will see later, in each of the deterministic and non-deterministic cases, how this model can be constructed.

[0095] Finally, in step (d), the candidate biomechanical model is validated or not based on the error model. We repeat that this is a validation for the patient's joint, i.e. we validate that the biomechanical model specifically reproduces this patient's joint in a sufficiently precise manner: it is not a question of globally validating a biomechanical model, but of ensuring that it is correctly adapted to the patient's joint in particular.

[0096] To do this, we advantageously predefine maximum uncertainty thresholds for each metric considered, and we check whether the uncertainty estimated by the error model is lower than the maximum tolerable uncertainty. If the uncertainties are acceptable (i.e. sufficiently low) for all the biomechanical metrics then the validation is successful, and we then speak of a validated biomechanical model. Preferably, we calculate, for each posture (i.e. each validation image) and for each metric considered, a confidence interval on the value of said metric, and the candidate biomechanical model is rejected (not validated) if the amplitude of at least a given number (in particular one, but potentially more if we accept a certain tolerance) of the calculated confidence intervals exceeds said uncertainty threshold of the metric considered. Thus a model can be validated for all or only a subset of the biomechanical metrics.

[0097] More precisely, for each biomechanical metric m considered for step (d), by confidence interval (CI) of level p (in [0, 1]) we mean the narrowest interval such that the probability that the value of the predicted metric lies in this CI interval is p. The value of p is chosen according to the criticality of the metric in therapeutic decision-making, e.g., for critical metrics, p can be set to 0.95.

[0098] The "randomness" of a metric's value arises from two factors: 1) a possibly non-deterministic biomechanical model whose particular outputs are not fixed values ​​but are rather defined as probability distributions; and 2) a non-deterministic error model that affects every simulation outcome.

[0099] For each simulation, the probability density of the value of a biomechanical metric M as a random variable is statistically estimated, yielding a mean value and a variance. Assuming that M follows a normal distribution, its mean and variance are used to determine the minimum and maximum bounds of the confidence interval, given an expected confidence level p. The width of the CI, is the difference between the upper and lower bounds of the interval, width = (max - min). If the width is large, then the uncertainty in M ​​is high; if the CI is narrow, then the uncertainty is small. The smaller the uncertainty, the greater the confidence in the model prediction. Candidate biomechanical models leading to an excessive level of uncertainty (excessive width of the CI) should be rejected.

[0100] If the model is validated, it can simply be returned to the interface 13, or used in a medical application as we will see later.

[0101] Otherwise, the method may comprise an optional step (e) of revising the candidate biomechanical model if it is not validated, then repeating steps (b) to (d) based on the revised biomechanical model as a new candidate biomechanical model, and so on iteratively until a validated model is obtained or the modeling procedure is abandoned.

[0102] Step (e) may require a new initialization of the biomechanical model, using a new initialization image and / or modifying parameters of the initialization procedure (such as the fineness of the finite element discretization of the deformable parts). In this case, this step (e) returns the protocol to step (a2) (see dotted arrow in Figure 2). Alternatively, step (e) can be done without modifying the model as it was initialized in step (a). In this case, step (e) consists of refining one or more parameters of the model (e.g., elasticity modulus of a ligament fiber) so that the behavior of the model is more faithful to reality, and for this, it is necessary to return to level (b) of the protocol (see solid arrow in Figure 2).

[0103] Note that step (e) can be systematically implemented if the candidate model is not validated, or only if the error remains limited. For example, we predefine maximum revision thresholds (larger than the maximum uncertainty thresholds) for each metric considered, and we check whether the error model is compatible with them (for example, if at least the said given number of calculated confidence intervals exceeds the said uncertainty threshold of the metric, but no calculated confidence interval exceeds the said revision threshold of the metric).

[0104] To summarize, in a preferred mode:

[0105] - if the error (width of the confidence intervals) is lower than the uncertainty thresholds ■> the model is validated

[0106] - if the error (width of the confidence intervals) is between the error thresholds and the revision thresholds ■> the model is revised

[0107] - if the error (width of the confidence intervals) is beyond the revision thresholds ■> the model is too erroneous to be revisable, and the process is restarted, in particular by acquiring new sets of medical images and a completely new candidate model is generated.

[0108] Thanks to this process, we can ensure that a validated model respects reality within a predefined precision corridor and that we can therefore use it, for example, to plan an operation or design a prosthesis.

[0109] The method may thus finally comprise a step (f) of using the validated biomechanical model, in a medical application, in particular for a simulation as implemented in step (b), this time in which said joint has a target posture, for example to estimate values ​​of said biomechanical metrics in this posture. Indeed, the validation guarantees that the model can be used in the entire range of postures, including outside the first, second and third sets.

[0110] Note that step (f) can use the error model constructed in step (c) to determine the maximum uncertainty on these estimated values ​​of the biomechanical metrics (i.e. the precision corridor mentioned just before). The idea is to allow complete risk management (taking into account in particular a "worst-case scenario"), which is essential in a critical use of the biomechanical model, for example before a surgical operation. It should be noted that in practice, at the end of step (c), individualized error models are obtained, i.e. associated with isolated validation images (and therefore postures in the modeling space).In order to extend the error modeling to the entire biomechanical modeling space (the space defined by the input variables of the biomechanical model), it is possible to assume that the parameters of the error models vary continuously in this space and interpolate (N-linear interpolation according to the dimension of the error model, b-splines or other).

[0111] Note that in the case of the presence of step (f), the present method may be considered as a method of simulating a target posture of the joint (and generally of exploiting the biomechanical model in a medical application) rather than just as a method of modeling the joint.

[0112] Non-deterministic mode

[0113] In this non-deterministic mode, typically corresponding to a “fuzzy” biomechanical mode, the model outputs including the metrics are probabilistic, and therefore statistical processing must be implemented.

[0114] In step (b), for each validation image a predetermined number Ns of simulations is advantageously implemented and a Monte-Carlo type approach is preferentially followed. The output is a collection of simulated values ​​of said biomechanical metrics for the posture considered (that of the validation image).

[0115] In the case of a discrete collection of postures (but the person skilled in the art will know how to transpose to the continuous case, see before), this collection is noted {L(i,m,s)}, with i the index of the posture, with 0 <i<Np (i.e. l’image de validation est h eE1 ), m l’indice de la métrique biomécanique avec 0<ITI<NM et s l’indice de la simulation avec 0<s<Ns. Dans l’image de validation h, la valeur correcte de la métrique biomécanique est connue, et notée R(i,m).

[0116] We can construct an error vector E (for example of dimension 3 in the case where the metric is a position) with E(i,m,s)=L(i,m,s)-R(i,m), of which we can take a norm (to make it a scalar) with a norm function such as the norm 2 (but also the norm 1 or the infinite norm), i.e. norm(E(i,m,s))=||L(i,m,s)-R(i,m)||.

[0117] The error model can be constructed in step (c) as a statistical model of E (vector quantity) or norm(E) (scalar quantity) based on all samples corresponding to the various metrics and images.

[0118] In both cases, we can assume that this quantity follows a normal distribution (in view of the central limit theorem) such that:

[0119] - for norm(E) (scalar quantity), the mean and variance can be estimated conventionally,

[0120] - for E (vector quantity) the density function can be estimated for example by implementing a PCA (Principal Component Analysis).

[0121] We will now consider two examples of biomechanical metrics:

[0122] - the distance between two anatomical points;

[0123] - the angle formed by three anatomical points.

[0124] Example of the distance between two anatomical points

[0125] As explained before, we determine the two collections L1 = {L(i,1 ,s)} and L2 = {L(i,2,s)} corresponding respectively to the positions of each of the two anatomical points in the Ns simulations, and E1 , E2 and / or norm(E1 ), norm(E2).

[0126] For each posture, we refer to the statistical charts in order to calculate a predefined number NE of errors for E1, E2 and / or norm(E1), norm(E2) following the distribution. Each error is then added to each simulated value so as to obtain a collection of NS*NE realizations for the positions of each of the two anatomical points.

[0127] As we want a distance here, we calculate all the distances corresponding to all the possible pairs of the realizations obtained for the positions of each of the two anatomical points, we therefore obtain (NS*NE) 2 distance values.

[0128] A new statistical analysis can be implemented on all the distance values ​​obtained (since in a perfect model we would always obtain the same value), in particular by estimating the mean and the variance. We can then calculate a confidence interval.

[0129] If for at least the said given number of postures (in particular only one), the width of the said confidence interval exceeds the said maximum uncertainty threshold, the model is rejected / revised (see above).

[0130] Example of the angle defined by three anatomical points

[0131] As explained before, we determine the three collections L1 = {L(i,1 ,s)}, L2 = {L(i,2,s)} and L3 = {L(i,3,s)} corresponding respectively to the positions of each of the two anatomical points in the Ns simulations, and E1 , E2, E3 and / or norm(E1 ), norm(E2), norm(E3).

[0132] For each posture, we then calculate a predefined number NE of errors for E1, E2, E3 and / or norm(E1), norm(E2), norm(E3) following the distribution and each error is added to each simulated value so as to obtain a collection of NS*NE realizations for the positions of each of the three anatomical points.

[0133] As we want an angle here, we calculate all the angles corresponding to all the possible triplets of the realizations obtained for the positions of each of the three anatomical points, we therefore obtain (NS*NE) 3 angle values.

[0134] A new statistical analysis can be implemented on all the angle values ​​obtained (since in a perfect model we would always obtain the same value), in particular by estimating the mean and the variance. We can then calculate a confidence interval.

[0135] If for at least the said given number of postures (in particular only one), the width of the said confidence interval exceeds the said maximum uncertainty threshold, the model is rejected / revised (see above).

[0136] Deterministic mode

[0137] In this deterministic mode, typically corresponding to a biomechanical mode in which all parameters and laws have well-defined unique values, the model outputs and therefore the corresponding metrics are unique.

[0138] In step (b), for each validation image a single simulation is advantageously implemented. The output is a collection of simulated values ​​of said biomechanical metrics for the posture considered (that of the validation image).

[0139] In the case of a discrete collection of postures (but the person skilled in the art will know how to transpose to the continuous case, see before), this collection is noted {L(i,m)}, with i the index of the posture, with 0 <i<Np (i.e. l’image de validation est h eE1 ), m l’indice de la métrique biomécanique avec 0<ITI<NM.

[0140] In the validation image h, the correct value of the biomechanical metric is known, and denoted R(i,m).

[0141] This time we take directly a norm of the error (to make it a scalar) with a norm function such as the norm 2 (but also the norm 1 or the infinite norm), which we note maxE(i,m))=||L(i,m)-R(i,m)||.

[0142] Indeed, we have only one value per metric and per posture, so we cannot deduce a probability density. Thus, we consider that the error observed at each posture is the maximum error of the candidate model. In other words, we assume a uniform distribution.

[0143] We will now again consider the two cases of biomechanical metrics: - the distance between two anatomical points

[0144] - the angle formed by three anatomical points.

[0145] Example of the distance between two anatomical points

[0146] We only have to determine the two collections L1 = {L(i,1 )}, L2 = {L(i,2)} corresponding respectively to the positions of each of the two anatomical points, which only include one value per validation image, and maxE(i,1 ), maxE(i,2).

[0147] With reference to Figure 4a, we can simply use geometric modeling to directly calculate the confidence interval, by representing the said two anatomical points by two spheres with center L(i, 1 ) and L(i ,2), and with respective radius maxE(i,1 ) and maxE(i,2).

[0148] The limits of the confidence interval then correspond to the min and max distances between two points of the two spheres: max = d(L(i,1 ) ;L(i,2)) + maxE(i,1 ) + maxE(i,2), and min = d(L(i,1 ) ;L(i,2)) - maxE(i,1 ) - maxE(i,2)

[0149] If for at least the said given number of postures (in particular only one), the width of the said confidence interval exceeds the said maximum uncertainty threshold, the model is rejected / revised (see above).

[0150] Example of the angle defined by three anatomical points

[0151] We only have to determine the three collections L1 = {L(i,1 )}, L2 = {L(i,2)}, L3 = {L(i,3)} corresponding respectively to the positions of each of the three anatomical points, which only include one value per validation image, and maxE(i,1 ), maxE(i,2), maxE(i,3).

[0152] Referring to Figure 4b, we can again use geometric modeling to directly calculate the confidence interval, by representing the said three anatomical points by three spheres with centers L(i, 1), L(i, 2) and L(i, 3), and with respective radii maxE(i, 1), maxE(i, 2) and maxE(i, 3). In the example shown, the vertex of the angle is arbitrarily the second anatomical point.

[0153] The limits of the confidence interval then correspond to the min and max angles defined by three points of the three spheres. A numerical optimization is this time necessary to find these min and max angles.

[0154] If for at least the said given number of postures (in particular only one), the width of the said confidence interval exceeds the said maximum uncertainty threshold, the model is rejected / revised (see above).

[0155] Server

[0156] According to a second aspect, the invention relates to the server 1 for implementing the method according to the first aspect.

[0157] 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 modeling a patient's joint.

[0158] The data processing means 11 are configured to implement steps consisting of:

[0159] - Obtaining a candidate biomechanical model of said joint and a first set of medical images of said joint, representing said joint in a posture of a first set of postures, called validation images;

[0160] - For at least one medical image of said first set of medical images of said joint, implementing at least one simulation of the candidate biomechanical model in which said joint has the same posture as in said medical image of said first set of images;

[0161] - Constructing an error model of the candidate biomechanical model by comparing, for at least one biomechanical metric of said joint and for at least one medical image of said first set of medical images of said joint for which at least one simulation has been implemented, the values ​​of said biomechanical metric in said medical image and in the simulation(s) implemented for said medical image;

[0162] - Validate or not the candidate biomechanical model depending on the error model.

[0163] 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).

[0164] The data processing means 11 are then further configured to:

[0165] - obtaining from the medical imaging device 10 said first set of medical images of said joint, as well as a second set of medical images of said joint, representing said joint in a posture of a second set of postures (and potentially a third set of medical images of said joint, representing said joint in a posture of a third set of postures);

[0166] - generate said candidate biomechanical model from the second set of medical images; and preferably

[0167] - calibrating said candidate biomechanical model based on said third set of medical images.

[0168] The data processing means 11 can also be configured to:

[0169] - revise the candidate biomechanical model if it is not validated; or

[0170] - use the validated biomechanical model, by implementing at least one simulation of this model in which said joint presents a target posture. Computer program product

[0171] 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 modeling a joint of a patient, 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

CLAIMS 1. Method for modeling 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: (a) Obtaining a candidate biomechanical model of said joint and a first set of medical images of said joint, representing said joint in a posture of a first set of postures, called validation images; (b) For at least one medical image of said first set of medical images of said joint, implementing at least one simulation of the candidate biomechanical model in which said joint has the same posture as in said medical image of said first set of images; (c) Building an error model of the candidate biomechanical model by comparing, for at least one biomechanical metric of said joint and for at least one medical image of said first set of medical images of said joint for which at least one simulation has been implemented, the values ​​of said biomechanical metric in said medical image and in the simulation(s) implemented for said medical image; (d) Validation or not of the candidate biomechanical model depending on the error model.

2. Method according to claim 1, wherein step (a) comprises sub-steps (a1) of obtaining said first set of medical images of said joint, as well as a second set of medical images of said joint, representing said joint in a posture of a second set of postures; and (a2) of generating said candidate biomechanical model from the second set of medical images.

3. The method of claim 2, wherein the first set of postures and the second set of postures are distinct.

4. Method according to one of claims 2 and 3, wherein step (a1) also comprises obtaining a third set of medical images of said joint, representing said joint in a posture of a third set of postures; step (a) comprising a sub-step (a3) ​​of calibrating the candidate biomechanical model as a function of said third set of medical images.

5. The method of claims 3 and 4 in combination, wherein the first set of postures and the third set of postures are distinct; and the second set of postures and the third set of postures are different but not necessarily distinct.

6. Method according to one of claims 2 to 5, in which step (a1) comprises the acquisition of the second set of medical images, and where appropriate of a third set of medical images, by a medical imaging device (10).

7. Method according to one of claims 1 to 6, in which step (d) comprises the calculation, for the biomechanical metric(s) and the medical image(s) of the first set, of a confidence interval on the value of said biomechanical metric from the error model, and the candidate biomechanical model is not validated if a width of at least a given number of the calculated confidence intervals exceeds an uncertainty threshold of the metric.

8. Method according to claim 7, wherein the values ​​of said biomechanical metric in said medical image and in the simulation(s) implemented for said medical image are calculated in step (c) as a function of the positions of characteristic anatomical points of said articulation in said medical image and in the simulation(s) implemented for said medical image.

9. The method of claim 8, wherein there is a plurality of characteristic anatomical points of said joint, and said biomechanical metric is a distance between two of said characteristic anatomical points of said joint or an angle defined by three of said characteristic anatomical points of said joint.

10. Method according to one of claims 1 to 9, comprising a step (e) of revising the candidate biomechanical model if it is not validated, then repeating at least steps (b) to (d) on the basis of the revised biomechanical model as a new candidate biomechanical model.

11. Method according to one of claims 1 to 10, comprising a step (f) of using the validated biomechanical model, comprising the implementation of at least one simulation of the validated biomechanical model in which said joint has a target posture.

12. The method of claim 11, wherein step (f) comprises using said error model to assess a level of uncertainty in the result of said simulation of the validated biomechanical model.

13. Method according to one of claims 1 to 12, wherein either said candidate biomechanical model is non-deterministic, and in step (b) for each medical image of said first set a plurality of simulations is implemented; or said candidate biomechanical model is deterministic, and in step (b) for each medical image of said first set a single simulation is implemented.

14. Server (1) for modeling a patient's joint, characterized in that it comprises data processing means (11) configured to: - Obtaining a candidate biomechanical model of said joint and a first set of medical images of said joint, representing said joint in a posture of a first set of postures, called validation images; - For at least one medical image of said first set of medical images of said joint, implementing at least one simulation of the candidate biomechanical model in which said joint has the same posture as in said medical image of said first set of images; - Constructing an error model of the candidate biomechanical model by comparing, for at least one biomechanical metric of said joint and for at least one medical image of said first set of medical images of said joint for which at least one simulation has been implemented, the values ​​of said biomechanical metric in said medical image and in the simulation(s) implemented for said medical image; - Validate or not the candidate biomechanical model depending on the error model.

15. System comprising a server (1) according to claim 14 and a medical imaging device (10), the data processing means (11) being further configured to: - Obtaining from said medical imaging device (10) said first set of medical images of said joint, as well as a second set of medical images of said joint, representing said joint in a posture of a second set of postures; - generate said candidate biomechanical model from the second set of medical images.

16. Computer program product comprising code instructions for executing a method according to one of claims 1 to 13 for modeling a patient's joint, when said program is executed on a computer.

17. Storage means readable by computer equipment on which is recorded a computer program product comprising code instructions for the execution of a method according to one of claims 1 to 13 for modeling a patient's joint.

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