A computer-implemented method for determining the behavioral and loading parameters of soft tissue from a plurality of images acquired in different vertical orientations.

Abstract

Computer-implemented method for determining behavioral and loading parameters of soft tissue from a plurality of images acquired in different vertical orientations. The invention relates to a computer-implemented method for determining parameters comprising a soft tissue stiffness field ( ) and a loading parameter ( ) applied to the soft tissue, in particular a pressure field, in which the values ​​( ), of said parameters are determined from at least two images of this soft tissue oriented in at least two different positions relative to the vertical direction, allowing the values ​​( ), , of said parameters to be determined so as to minimize a discrepancy between the deformations of at least a part of the soft tissue observed from the images and the corresponding deformations determined by a model ( ) of the soft tissue that depends on said parameters. Figure for the abstract: Fig. 1

Description

Title of the invention: Computer-implemented method for determining behavior and loading parameters of soft tissue from a plurality of images acquired in different vertical orientations Technical field

[0001] The present invention relates to the field of estimating behavioral and loading parameters of soft tissue models from images.

[0002] The invention relates more specifically to a computer-implemented method for determining a stiffness field of a soft structure and a loading parameter such as a force or pressure field applied to this structure, combining several images acquired in different orientations.

[0003] The main field of application envisaged is biomedical engineering, more specifically personalized digital modeling applied to the diagnosis, classification, prognosis and treatment of patients. The invention is particularly suitable for the in vivo and non-invasive estimation of stiffness and pressure applied to soft living tissues.

[0004] More generally, the invention can be applied to all objects or soft tissues, whether human, animal or plant, to non-invasively estimate internal rigidities and pressures, as well as other parameters inherent to a model, from volume images, without requiring force measurement. Prior art

[0005] The construction of digital models of biological tissues is an active field of biomechanics. Such models can indeed provide medical personnel with reliable tools to help in the prognosis or diagnosis of pathologies as well as in the control of the progress of medical treatments. Personalized digital models, also called "digital twins", are particularly advantageous. They consist of coupling the physical modeling of a tissue with specific data obtained on a patient in order to obtain a precise, objective and quantitative vision of the state of this patient.

[0006] The creation of a digital model of a tissue is based on the definition of a constitutive law, which describes the behavior of the modeled tissues and involves so-called constitutive material parameters such as the stiffness of the tissue, in combination with a loading, i.e. the stresses to which the tissue is subjected. The loading involves parameters such as the force or pressure field imposed on the tissue that are typically either set to standard physiological values ​​empirically or estimated from information extracted from data collected on the tissue.

[0007] For the construction of digital twins, it is generally not possible to identify all parameters of a complex tissue or organ model from clinical images. Therefore, it is often necessary to fix parameters to physiological values.

[0008] This solution is, however, unsatisfactory. Indeed, the material parameters as well as the loading parameters, in particular the internal pressure field when present, vary very greatly from one individual to another. In addition, the physiological data generally come from ex vivo experiments, possibly conducted on animals, which introduces a significant bias into the experimental parameter values ​​obtained.

[0009] The use of acquired data is therefore important for the production of personalized digital models, making it possible in particular to take into account the great variability of parameters between individuals. Estimating parameters from measurements, when possible, remains the most reliable solution for the construction of data-based models.

[0010] However, it is generally not possible to identify constitutive parameters or loading parameters solely from images, since a force measurement is necessary to supplement the kinematic data present in the images. In particular, the absence of internal force measurements in the tissue prevents the correct identification of the constitutive parameters.

[0011] In particular, it is generally difficult to measure the value of the internal pressure applied to certain tissues, even though this pressure can constitute an important biomarker for the diagnosis and prognosis of pathologies. This is for example the case of the lung, subjected to pleural pressure, that is to say a negative pressure keeping the lungs inflated, for which an in vivo measurement is very difficult. The classic method of measuring this pressure consists of the use of esophageal balloons. This method is however both too imprecise and too invasive to be carried out in routine intervention.

[0012] The article Visentin, F., Groenhuis, V., Maris, B., Dall'Alba, D., Siepel, F., Stramigioli, S. & Fiorini, P. (2019). Iterative simulations to estimate the elastic properties from a series of MRI images followed by MRI-US validation. Medical & Biological Engineering & Computing describes the use of images obtained by MRI in the context of breast deformation modeling to estimate the stiffness of a physical reproduction of a breast. The images are obtained by placing the breast model in two different positions. The deformation of the model is due solely to the gravity. The comparison between the images obtained allows the estimation of the rigidity of the model.

[0013] At equilibrium, the remote forces, here gravity, balance with the contact forces, also called reaction forces, exerted by the surrounding systems. Reaction forces are not considered in this article. Furthermore, the boundary conditions at the base of the breast are not representative of real physiological conditions because the displacements are completely blocked. Therefore, it is not possible to correctly estimate the reaction forces. Furthermore, the described method is not applicable to the case of strongly moving tissues. The edges of a lung, for example, move strongly between the end-of-expiration configuration and the end-of-inspiration configuration.

[0014] Thus, the solution described is not intended to estimate the loading to which the organ studied is subjected.

[0015] There is therefore a need to propose methods for estimating behavioral parameters but also loading parameters, allowing the construction of more reliable digital twins.

[0016] The aim of the invention is to meet this need. Statement of the invention

[0017] To do this, the invention relates to a computer-implemented method for determining parameters comprising a stiffness field of a soft tissue (?) and a loading parameter (P) applied to the soft tissue, in particular a pressure field, in which the values ​​(al, pl) of said parameters are determined from at least two images of this soft tissue oriented in at least two different respective positions relative to the vertical direction, making it possible to minimize a difference between the deformations of at least one part of the soft tissue observed from the images and the corresponding deformations determined by a model (( / ^ p)) of the soft tissue which depends on said parameters.

[0018] al and pl are thus values ​​taken by the fields ? and P. The parameters al and pl can be determined for the whole of the soft tissue or for a part of the soft tissue.

[0019] Thus, in the invention, it is possible to use a plurality of images, preferably biomedical, of a soft tissue placed in at least two different orientations relative to the vertical direction so as to use gravity, which is a perfectly known force, to identify several parameters of behavior, including at least the rigidity, and of loading, in particular the pressure, of a model of soft tissue subjected to loading.

[0020] By implementing the method according to the invention, the differences observed between the images obtained in different positions are mainly induced by the gravity and can be used, in an inverse problem, to estimate tissue behavior and imposed loading.

[0021] By "soft tissue" is meant an organic tissue on which gravity will have a significant effect. In other words, gravity causes a significant deformation of a soft tissue when its orientation is modified, for example a deformation of amplitude greater than or equal to 1%, 5% or 10% of at least one dimension of the soft tissue between two different orientations. A soft tissue can in particular be a muscle, an organ or a fibrous tissue.

[0022] In an in vivo situation, pressure is difficult to measure non-invasively. The invention advantageously makes it possible to estimate not only the unloaded configuration of the organ and the stiffness of the tissue, but also the loading to which the organ is subjected. This makes it possible, in particular, to construct better quality digital twins.

[0023] The invention also makes it possible to obtain more reliable values ​​of the parameters which can be estimated by existing methods.

[0024] Depending on the numerical models U(a, p] implemented, the parameterization of the stiffness field "can be a scalar parameter or several parameters, possibly spatialized, which can constitute a field of values. Similarly, the parameterization of the applied load P can be a scalar parameter or several parameters, possibly spatialized, which can constitute a field of values.

[0025] According to an advantageous characteristic, at least one displacement field jjmeus is determined from the images of the soft tissue. The displacement field y1™™ characterizes the deformation of the soft tissue between two positions by characterizing the changes in position of each material point between two images.

[0026] Preferably, the determination of the values ​​al, pl of parameters minimizing said deviation is carried out by minimizing a function p^— || U(a, p) - Umeas || , which corresponds to the displacement method. Other methods (deviation from equilibrium, error in behavior relation, virtual field method, etc.) can also be used.

[0027] The displacement field ymeas may characterize the deformation of the entire soft tissue and may be fully determined, for example by image correlation method, before the determination of al and pl; alternatively, y™1™, «1 and pl may be determined in a single integrated correlation or data assimilation step. The displacement field may also be determined locally, i.e. on only one or more parts of the soft tissue, and the values ​​of al and pl may be obtained for only these parts of the tissue. soft.

[0028] Advantageously, the determination of the values <zl, pl de paramètres minimisant ledit écart est réalisée par l’application d’un modèle statistique, tel qu’un modèle de type réseau de neurones, aux images du tissu mou ou à un champ de déplacement jjmm\ jjtneas déterminé à partir des images du tissu mou.

[0029] The statistical model used is configured, in particular trained, to determine the values ​​al and pl either from the images of the soft tissue or from the displacement fields extracted from the images.

[0030] The statistical model may in particular be a physics-informed neural network (PINN), particularly suitable for solving inverse problems incorporating physical data. The neural network may be trained by adapting the internal weights of the network so that it produces a good input-output relationship between the input data (which may be soft tissue images or the displacement fields obtained from soft tissue images) and the results, i.e. the al and pl values. To this end, the neural network is evaluated for a large number of input data. The physical model of the soft tissue as well as the cost function characterizing the deviation between the model and the data are evaluated. The cost function is minimized by adapting the weights of the neural network.Once trained, the neural network is able to very quickly estimate the al and pl values ​​associated with a displacement field or images.

[0031] According to an advantageous characteristic, the method comprises, before determining the values ​​ql, pl of parameters minimizing said difference, a step of acquiring images of the soft tissue, in which the soft tissue is placed in a first position to acquire a first image then in a second position oriented differently with respect to the vertical direction to acquire a second image.

[0032] Preferably, the images are obtained by computed tomography, ultrasound and / or magnetic resonance imaging (MRI). More preferably, the soft tissue is an organ of a patient. The images of the soft tissue may in particular be acquired in vivo on the patient positioned at least in supination and pronation. The method may comprise the acquisition of the images.

[0033] The two images acquired with the soft tissue in different orientations correspond, for example, to images where the soft tissue has undergone a significant rotation between the two images, for example greater than 30°, in particular 90° or 180°. The method may comprise the step of modifying the orientation of a support on which the soft tissue rests, in a controlled manner, the acquisition of the images being carried out in connection with the control of the orientation of the support; the latter is, for example, a table on which a patient may rest.

[0034] The modification of the orientation can be carried out around one or two horizontal geometric axes of rotation.

[0035] According to one embodiment of the invention, the soft tissue is a lung, a brain or a breast. The loading parameter may in particular be the pleural pressure in the case of the lung and the cerebral pressure in the case of the brain.

[0036] The invention also relates to a system for imaging the human or animal body configured to enable the acquisition of images of soft tissue of said body positioned in at least two different positions relative to the vertical, and comprising a processor executing a program making it possible to determine at least from these images said values ​​"1 and pl by implementing the method according to the invention, as defined above.

[0037] The imaging system may be a tomographic, ultrasound or MRI imaging system.

[0038] It may comprise a surface for receiving the body whose orientation relative to the vertical can be modified, in particular automatically by the system, so as to change the orientation of the body between the acquisitions of the different images. This surface is for example a table rotating around one or two horizontal axes and capable of taking two differently oriented positions, for example at 90° to each other, for example each at 45° to the vertical.

[0039] The invention also relates to a computer program product comprising a code which, when executed on a processor, makes it possible to implement the different steps of the method according to the invention, as defined above.

[0040] The invention also relates to a simulator of the mechanical behavior of a soft tissue, comprising a digital twin of a soft tissue obtained by implementing the method according to the invention as defined above, this soft tissue being in particular a lung or the brain, and this digital twin being recorded in a computer memory. Such a simulator may comprise any computer system making it possible to exploit all of the data constituting the digital twin, in particular a microcomputer and / or a server, as well as an interface making it possible to interface this twin with a CAD tool for example.

[0041] The invention also relates to a method for manufacturing soft tissue protection equipment, in which a simulator as defined above is used in a phase of modeling the equipment to determine the mechanical stresses of the tissue in the event of mechanical stress through the equipment, and the equipment is manufactured after such a modeling phase. The modeling phase makes it possible, for example, to determine the shape and the material(s) of the equipment leading to optimization of the protection of the soft tissue, depending on manufacturing constraints for example. Brief description of the drawings

[0042] [Fig.l] [Fig.l] represents different image acquisition schemes of a lung.

[0043] [Fig.2] [Fig.2] is a graph representing the distribution of the error of identifying the stiffness of a structure as a function of the measurement noise, the identification being obtained by a known method using two supine images, where the stiffness and the loading are identified together.

[0044] [Fig.3] [Fig.3] is a graph representing the distribution of the error identification of the pressure applied to a structure as a function of the measurement noise, the identification being obtained by a known method using two supine images, where the stiffness and the loading are identified together.

[0045] [Fig.4] [Fig.4] is a graph representing the distribution of the error of identifying the stiffness of a structure as a function of the measurement noise, the identification being obtained by a known method using two prone images, where the stiffness and the loading are identified together.

[0046] [Fig.5] [Fig.5] is a graph representing the distribution of the error identification of the pressure applied to a structure as a function of the measurement noise, the identification being obtained by a known method using two prone images, where the stiffness and the loading are identified together.

[0047] [Fig.6] [Fig.6] is a graph representing the distribution of the error for identifying the stiffness of a structure as a function of measurement noise, the identification being obtained by a method according to the invention using two prone images and two supine images, where the stiffness and the loading are identified together.

[0048] [Fig.7] [Fig.7] is a graph representing the distribution of the error identification of the pressure applied to a structure as a function of the measurement noise, the identification being obtained by a method according to the invention using two prone images and two supine images, where the stiffness and the loading are identified together.

[0049] [Fig.8] [Fig.8] is a graph representing the distribution of the error on the identified stiffness of a lung as a function of noise as obtained by a known determination method using a supine image, the loading being known.

[0050] [Fig.9] [Fig.9] is a graph representing the distribution of the error on the identified lung stiffness as a function of noise as obtained by a known determination method using a prone image, the loading being known.

[0051] [Fig. 10] [Fig. 10] is a graph representing the distribution of the error on the identified stiffness of the lung as a function of noise as obtained by a method of determination using a prone image and a supine image, with the loading known.

[0052] [Fig. 11] [Fig. 11] represents an imaging system according to the invention. Detailed description

[0053] In the context of the invention, the vertical direction is a direction parallel to the gravity field.

[0054] In an advantageous embodiment, the invention is implemented in the context of the construction of a digital twin of a lung.

[0055] Figure 1 represents different diagrams for acquiring images of a lung for implementing the method according to the invention. The orientation of the patient is defined by the arrow denoted g indicating the direction of the gravitational field. An arrow pointing downwards in the figure corresponds, for example, to a pronation (or procubitus) position of the patient while an arrow pointing upwards in the figure corresponds to a supination (or decubitus) position. The configurations of the lung at different times between the states of maximum expiration and maximum inspiration are denoted pi to pn. The states pe and p; correspond respectively to the configuration of the lung in maximum expiration and maximum inspiration.The displacement field between two states pa and pb is noted u1^ in the case of two states in pronation, in the case of two states in supination and in the case of two states p,, the starting state being in the pronation position and the arrival state being in the supination position.

[0056] In the case of the lung, the deformation of the organ can be considered as being exclusively due on the one hand to pleural pressure, negative pressure ensuring that the lung remains inflated, and on the other hand to gravity, whose influence on the deformation is less compared to pleural pressure but nevertheless notable. Since the deformation of the lung is particularly sensitive to pleural pressure, it is important to have access to its precise value. Tissue stiffness is also a parameter that is important to identify in the context of this example. Indeed, stiffness could constitute an important biomarker allowing the diagnosis and prognosis of pulmonary diseases such as fibrosis. Two stiffnesses are then particularly interesting: healthy stiffness and fibrotic stiffness, higher due to the stiffening of the tissues induced by fibrosis.

[0057] In cases of lung disease, the healthcare staff generally routinely acquires two images of the patient's lungs, both taken with the patient in the same position: one image at the end of expiration, and one image at the end of inspiration. This corresponds to case A shown in [Fig.l].

[0058] Case A does not allow the estimation of pleural pressure, healthy stiffness and fibrotic stiffness at the same time, but only two of these quantities, for example healthy stiffness and fibrotic stiffness.

[0059] The method according to the invention uses images acquired in different positions of the patient, which in particular also makes it possible to estimate pleural pressure.

[0060] Case B presented in [Fig.l] corresponds to the acquisition of three images: one image in the state of maximum inspiration in the pronation position and two images in the state of maximum expiration, one in the pronation position and the other in the supination position.

[0061] Case C presented in [Fig.l] corresponds to the acquisition of four images: two images in a state of maximum inspiration and two images in a state of maximum expiration, one in a pronation position and the other in a supination position.

[0062] The use of a plurality of images, taken on a patient placed in at least two different vertical orientations, for example prone and decubitus, makes it possible to obtain more information on the behavior of the tissues and therefore to increase the number of identifiable parameters, or the precision of the estimation.

[0063] Thus, the images obtained in case B make it possible to obtain the field of displacements between the configuration at the end of expiration and at the end of inspiration in pronation, as well as the field of displacements between the configuration at the end of expiration in pronation and the configuration at the end of expiration in supination, due solely to gravity. Similarly, case C makes it possible to obtain the field of displacements between the configuration at the end of expiration and at the end of inspiration in pronation, as well as the field of displacements between the configuration at the end of expiration and at the end of inspiration in supination. The difference between these two fields is solely due to gravity. The data are then assimilated into an adapted model, thus resulting in a personalized model, i.e. a digital twin.

[0064] A digital model, for example a finite element model, of the lung is then constructed from the information obtained from the images, in particular the geometry of the organ and the porosity field in this example. The images obtained provide access to the porosity field of the lungs. Considering that the latter are porous and that a solid phase comprising the tissues and the blood coexists with a fluid phase comprising the air circulating in the lungs, a so-called poromechanical law is advantageously formulated in this embodiment to model the lung.

[0065] The poromechanical law used can be that described in the publications Patte, C., Genet, M., & Chapelle, D. (2022). A quasi-static poromechanical model of the lungs. Biomechanics and Modeling in Mechanobiology, 21(2), 527-551, Patte, C., Brillet, PY, Fetita, C., Bemaudin, JF, Gille, T., Nunes, H.,... & Genet, M. (2022). Estimation of regional pulmonary compliance in idiopathic pulmonary fibrosis based on per-sonalized lung poromechanical modeling. Journal of Biomechanical Engineering, 144(9), 091008, and Laville, C., Fetita, C., Gille, T., Brillet, PY, Nunes, H., Bemaudin, JF, & Genet, M. (2023). Comparison of optimization parametrizations for regional lung compliance estimation using personalized pulmonary poromechanical modeling. Biomechanics and Modeling in Mechanobiology, 1-13.

[0066] Other laws may also be chosen depending on the compromise between accuracy and complexity of the desired model. For example, a hyperelastic law such as an Ogden-Ciarlet-Geymonat law or a Mooney-Rivlin law may be used. These laws are described in the publications Ogden, RW (1972). Large de-formation isotropy elasticity: On the correlation of theory and experiment for compressible rubberlike solids. Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences, 328(1575), 567-583, Ciarlet, PG, & Geymonat, G. (1982). On the behavior laws in compressible nonlinear elasticity. Comptes Rendus de l'Académie Des Sciences Série II, 295, 423—426, and Weiss, JA, Maker, BN, & Govindjee, S. (1996). Finite element implementation of incompressible, transversely isotropie hyperelasticity. Computer Methods in Applied Mechanics and Engineering, 135(1-2), 107-128.

[0067] The various parameters and the pleural pressure are then estimated via an estimation step. This step is based in this embodiment on the FEMU method, also known as the displacement method. However, other estimation methods can be used such as the equilibrium deviation method or the virtual field method. These methods are described in the publication Avril, S., Bonnet, M., Bretelle, A.S., Grédiac, M., Hild, F., lenny, P.,... & Pierron, F. (2008). Overview of identification methods of mechanical parameters based on full-field measurements. Experimental Mechanics, 48, 381-402.

[0068] Here we note B the behavior and loading parameters (including the applied pressure) to be identified.

[0069] The field of displacements between the configuration at the end of expiration and the configuration at the end of inspiration constitutes the measurement jjmeas. The objective of the estimation step with the FEMU method is to find the parameters Q which minimize the difference between ymecls and the field of displacements calculated with the numerical model of the lung which depends on the parameters B, which we denote by U( 9 ) ■

[0070] This is advantageously done by minimizing a function called the cost function j(f) = || U ( b ) - || . In this embodiment, J is a discrete function. This function can be minimized with a classical derivative-free optimization algorithm, but any known optimization method could also be used.

[0071] Other cost functions can be used to determine the parameters B optimal. They can notably be based on the principle of deviation from equilibrium or directly on the intensity of the images.

[0072] The articles Allaire, G. (2007). Numerical analysis and optimization: An introduction to mathematical modeling and numerical simulation. Oxford University Press and Bard, Y. (1974). Nonlinear parameter estimation (No. 04; QA276. 8, B3.) describe different methods for minimizing a cost function.

[0073] Alternatively, the parameters are estimated by implementing a statistical model, such as a neural network type model, to obtain the parameters directly from the soft tissue images or from the displacement field determined from the soft tissue images.

[0074] The method according to the invention is generalized to the case where there are more than two images and / or more than two orientations of the soft tissue relative to the vertical direction. The use of more than two images makes it possible to obtain a plurality of fields of displacements ymeas in |cs images two by two and thus to improve the precision of the estimation of optimal parameters 6, or even to enable the identification of additional parameters. Examples

[0075] In one example, synthetic data from a lung are used to validate the invention. If the invention makes it possible to identify parameters from real data measured on an individual, it is difficult to quantify the error made on the identified parameters because the exact values ​​corresponding to the real situation are not known. Thus, in this example, the inventors carried out the validation of the method according to the invention using synthetically generated data.

[0076] For this purpose, two synthetic measurements are created, one corresponding to a measurement of the displacement field between the end-of-expiration state and the end-of-inspiration state in the prone position and the other corresponding to a measurement of the displacement field between the end-of-expiration state and the end-of-inspiration state in the decubitus position. For this, the parameters 0 are set to physiological values ​​6$ and the associated displacement field is calculated via the numerical model of the lung used.

[0077] The displacement field obtained is disturbed by random Gaussian noise in order to take into account the noise characteristic of real measurements, the origin of which is diverse, coming for example from the imaging equipment used. The intensity of the disturbance is characterized by the signal-to-noise ratio, noted SNR. The smaller the SNR, the greater the impact of the noise on the images.

[0078] For a given SNR, several parameter estimations are carried out until the distribution of the identified parameter converges. The previously described optimization process is then applied.

[0079] In another example, a simplified linear spring model is used. This example corresponds to a highly identifiable case, for which the expected results are known. In this model, the displacement of the spring relative to an unloaded configuration depends on the ratio between the loading and the stiffness. The displacement between two positions of different vertical orientation depends on the orientation of the spring relative to gravity. Thus, the stiffness and the loading can take any value respecting the ratio u — £222 where u corresponds to the displacement, p to the loading, m to the mass, g to the acceleration of gravity and a to the stiffness, in the case of the prone position. In the case of the decubitus position, we obtain y — . The optimization process here amounts to finding parameters (a, p) which allow u(a, p) to be as close as possible to a given displacement uo. Thus, any loading P respecting the condition P = + m^, for any value of stiffness a, allows to obtain the measure wo. H therefore exists an infinity of couples ( <4 p) — au^ -p mgj satisfying u = Mo. H is therefore impossible to identify both the stiffness and the loading in the case of images obtained only on the back or only on the stomach.

[0080] The invention makes it possible to make these two parameters identifiable. Indeed, the difference between the displacement obtained in the case of decubitus and the displacement obtained in the case of procubitus is due to gravity. Using the images in both positions therefore makes it possible to access additional information, thus enabling the identification of stiffness and loading.

[0081] Figures 2 to 7 illustrate these results.

[0082] Figures 2 and 4 represent the distribution of the error, noted e, on the stiffness identified as a function of the measurement noise, noted SNR, by applying a determination method on supine images (curve fl, [Fig.2]) and on prone images (curve f3, [Fig.4]). [Fig.6] represents the distribution of the error e on the stiffness identified as a function of the SNR noise by applying the method according to the invention on prone and supine images (curve f5, [Fig.6]).

[0083] Figures 3, 5, 7 represent the distribution of the error, noted e, on the identified loading as a function of the measurement noise, noted SNR, by applying a determination method on images in the supine position (curve f2, [Fig.3]), on images in the prone position (curve f4, [Fig.5]), and by applying the method according to the invention on images in the supine position and prone position (curve f6, [Fig.7]).

[0084] The standard deviation o of the error distribution around the mean values ​​represented by the curves fl to f6 is also represented in each of Figures 2 to 7.

[0085] For each of Figures 2 to 7, curve d corresponds to the initial distribution, i.e. the values ​​to which the parameters are initialized before optimization. preferably initializes parameter values ​​in an interval close to the average parameter values, for example plus or minus 30% around a known average parameter value. This allows, in the case of in silico illustrations, to avoid an initialization systematically close to the exact solution and therefore to avoid distorted results; ultimately this corresponds to realistic cases of estimation where the real value is not known and cannot be used as initialization.

[0086] It is found that for low noise levels typical of real measurements (SNR varying from plus infinity to 10), it is possible to identify both stiffness and loading with the method according to the invention (curves f5, f6). However, identification becomes impossible for small SNRs, because in such cases, the measurement is completely disrupted by noise.

[0087] On the other hand, whatever the noise level, we note that it is impossible to correctly identify both the stiffness and the loading in the case of a single measurement in the supine position and in the case of a single measurement in the prone position: the curves fl to f4 do not converge towards the correct value of the stiffness and the loading.

[0088] Adding images in an additional position therefore makes it possible to identify an additional parameter and thus improve the models developed by making them more personalized to each patient.

[0089] For comparison, Figures 8 to 10 represent the distribution of the error, noted e, on the identified stiffness as a function of the measurement noise, noted SNR, for a loading assumed to be known, by applying a determination method on supine images (curve f7, [Fig.8]) and on prone images (curve f8, [Fig.9]), as well as by applying the method according to the invention on prone and supine images (curve f9, [Fig. 10]). It is clear from these graphs that a satisfactory identification of the stiffness is possible on the basis of a single image when the loading is known, the determination of the stiffness being improved by using both images. But, as illustrated in Figures 2 to 7, the identification of both the stiffness and the loading is not possible on the basis of a single image. The method according to the invention makes it possible to determine the stiffness and the loading in this case.

[0090] Other variants and improvements may be provided without departing from the scope of the invention.

[0091] In particular, the method according to the invention can be applied to a number of images of the soft tissue greater than two. The images can also be taken when the soft tissue is in different configurations. For example, a lung in vivo has a different configuration at the end of inspiration and at the end of expiration. As described with reference to [Fig.l], it is possible to compare two images of the lung at the end of inspiration and two images of the lung at the end of expiration, the images being taken in the prone and decubitus positions. It is also possible to use three images, as illustrated in case B of [Fig.l], for example an image at the end of expiration and an image at the end of inspiration in the prone position and an image at the end of expiration in the supine position.

[0092] It is possible to use a larger number of images to provide more detailed modeling of the soft tissue. This is particularly advantageous in the context of pulmonary fibrosis. Pulmonary fibrosis is characterized by non-homogeneous stiffening of the lung tissue. Thus, in fibrosed lungs there are several sections with different stiffnesses. By increasing the number of images used, the different stiffnesses can be better identified by making it possible to measure more displacement fields between two images among the images used.

[0093] The invention requires images of the soft tissue taken in at least two different orientations relative to the vertical direction. These orientations are not limited to pronation and supination positions. A soft tissue, or a patient for in vivo measurements, may be oriented at different angles relative to the vertical when taking images. For example, a patient may be lying on a table when taking images in pronation and / or supination, and the table may be held horizontally and / or inclined by rotation about one or two horizontal axes perpendicular to each other. The rotation of the table about a horizontal axis may in particular be between 0° and 45°. Advantageously, the movement of the table facilitates the acquisition of the different images and the positioning of the patient, in particular when the patient is with reduced mobility or unconscious.

[0094] [Fig. 11] represents an imaging system 10 according to the invention. The imaging system 10 can in particular be used to acquire images of soft tissue of an animal or a human and can be a tomographic, ultrasound or MRI imaging system. It comprises an imaging device 11 and a receiving surface 12, for example a table, intended to receive the patient 13.

[0095] The receiving surface is, in the example illustrated, movable in rotation around a horizontal axis so as to be able to take different positions in which the orientation of the patient 13 relative to the vertical direction is different.

[0096] The invention is not limited to the case of the lung. In particular, it also applies to the brain and facilitates the classification, diagnosis, prognosis and treatment of brain diseases. It can also facilitate the detection of head trauma via rapid estimation of cranial pressure.

[0097] The brain is composed of soft tissues, on which gravity has a significant influence. It is subjected to cranial pressure, the estimation of which in vivo, carried out via a lumbar puncture, is very invasive. Unlike the lung, for which a field of displacements is accessible in a single position (by comparing images at the end of expiration and at the end of inspiration, for example) thanks to the differential of pleural pressure, cranial pressure remains constant. The use of gravity therefore allows access to a displacement field which, thanks to the method according to the invention, allows the identification of both parameters such as tissue rigidity and cranial pressure.

[0098] The invention makes it possible to obtain a more reliable model of the brain via better identification of the model parameters. This can, for example, help in the sizing of sports equipment, in particular protective helmets for sports involving risks of head trauma such as rugby or American football. Indeed, the invention can help to estimate the increase in cranial pressure following an impact according to the configuration (material, dimensions, etc.) of the helmet.

[0099] More generally, the increase in pressure in the skull following an impact is a significant issue and is the subject of particular attention in the development of safety devices. For example, many safety devices in the automotive industry are developed using biomechanical models of the body and particularly of the human head. A better estimation of cranial pressure values ​​following an impact makes it possible to design more efficient safety devices.

[0100] Biomechanical modeling is an important step in the manufacturing of protective equipment. Indeed, it allows for testing and optimization in silico of the topology and geometry of this equipment, which reduces the costs associated with physical models. In addition, physical tests are carried out on dummies whose physical properties may differ from those of people, and they do not provide access to quantities of interest such as the increase in cranial pressure following an impact. Coupling a model of equipment, for example a helmet, with a model of the brain would improve access to this information. Indeed, modeling an impact on a helmet provides access to stresses transmitted to the brain, which then makes it possible to determine potential damage.Identifying stiffness and pressure parameters in the brain could therefore help optimize the manufacture of a personalized helmet that best protects people such as professional athletes.

[0101] More broadly, the method according to the invention can be applied to all objects or soft tissues, whether human, animal or plant, to non-invasively estimate internal rigidities and pressures from volume images without requiring force measurement. This has numerous applications such as the classification of diseases from identified pressure values, diagnostic assistance or the sizing of protective or safety equipment.

Claims

Claims

1. A computer-implemented method for determining parameters comprising a stiffness field of a soft tissue (?) and a loading parameter (P) applied to the soft tissue, in particular a pressure field, in which the values ​​(al, pi) of said parameters are determined from at least two images of this soft tissue oriented in at least two different respective positions relative to the vertical direction, making it possible to minimize a difference between the deformations of at least one part of the soft tissue observed from the images and the corresponding deformations determined by a pp model of the soft tissue which depends on said parameters.

2. Method according to claim 1, in which a displacement field ymeas is determined from the images of the soft tissue and the determination of the values ​​(al, pl) of parameters minimizing said deviation is carried out by minimizing a function j(a, p) = || U(a, p) - Umeas || •

3. Method according to claim 1, in which the determination of the values ​​(al, pl) of parameters minimizing said deviation is carried out by the application of a statistical model, such as a neural network type model, to the images of the soft tissue or to a displacement field determined from the images of the soft tissue.

4. Method according to one of the preceding claims, comprising before determining the values ​​(al, pl) of parameters minimizing said difference a step of acquiring images of the soft tissue, in which the soft tissue is placed in a first position to acquire a first image then in a second position oriented differently with respect to the vertical direction to acquire a second image.

5. Method according to the preceding claim, the images being obtained by computed tomography, by ultrasound echography and / or by magnetic resonance imaging.

6. Method according to the preceding claim, the soft tissue being an organ of a patient.

7. Method according to the preceding claim, the images of the soft tissue being acquired in vivo on the patient positioned at least in supination and in pronation.

8. A method according to any preceding claim, wherein the soft tissue is a lung, a brain or a breast.

9. Imaging system (10) of the human or animal body configured to allow the acquisition of images of a soft tissue of said body (13) positioned in at least two different positions relative to the vertical, and comprising a processor executing a program making it possible to determine at least from these images said values ​​((Zl, pi) of parameters by implementing the method according to any one of the preceding claims.

10. Imaging system according to claim 9, being a tomographic, ultrasound or MRI imaging system.

11. System according to claim 9 or 10, comprising a surface (12) for receiving the body whose orientation relative to the vertical can be modified, in particular automatically by the system, so as to change the orientation of the body between the acquisitions of the different images, this surface being in particular a table rotating around one or two horizontal axes and capable of taking two differently oriented positions, for example at 90° to each other, for example each at 45° to the vertical.

12. Computer program product comprising code which, when executed on a processor, implements the various steps of the method as defined in any one of claims 1 to 8.

13. Simulator of the mechanical behavior of a soft tissue, comprising a digital twin of a soft tissue obtained by implementing the method according to any one of claims 1 to 8, this soft tissue being in particular a lung or the brain, and this digital twin being recorded in a computer memory.

14. A method of manufacturing soft tissue protection equipment, in which a simulator as defined in claim 13 is used in a phase of modeling the equipment to determine the mechanical stresses of the tissue in the event of mechanical stress through the equipment, and the equipment is manufactured after such a modeling phase.

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