COMPUTER-IMPLEMENTED METHOD FOR ESTIMATING THE FRACTION OF CORONARY RESERVE FLOW, SYSTEM

Abstract

COMPUTER-IMPLEMENTED METHOD FOR ESTIMATING CORONARY RESERVE FLOW FRACTION, SYSTEM Method for estimating the coronary reserve flow fraction (FFR) of a vessel comprising: Acquisition (ACQ1) of a first image from an imaging system; Extraction (EXT1) of a first data set (ENS1) defining anatomical descriptors of a first vessel; Acquisition (ACQ2) of a second data set (ENS2) comprising at least the heart rate, the systolic pressure and the myocardial mass;Generation (GEN1) of an output (S1) defining a prediction of a quantity of coronary flow reserve fraction (FFR) by means of the execution of a first machine learning model (MLA1) to produce an output (S1), said first machine learning model (MLA1) implementing a parameterizable loss function including at least a first factor modeling at least one parameterized physical constraint optimized during the training of said model (MLA1), said parameterized physical constraint resulting in particular from a numerical model of hemodynamic equations (MOD1). Figure for the abstract: Fig.5;

Description

Title of the invention: COMPUTER-IMPLEMENTED METHOD FOR ESTIMATING THE FRACTION OF CORONARY RESERVE FLOW, SYSTEM Field of invention

[0001] The field of the invention relates to methods and systems for predicting a value of the coronary reserve called FFR for the characterization of coronary flow. The field of the invention relates more particularly to non-invasive methods implementing software means for characterizing coronary flow. The invention relates to means providing decision support for the placement of a stent, the invasive deepening of a pathology or on the contrary to rule out a risk of infarction for example. State of the art

[0002] Currently, the characterization of coronary flow in a patient, in particular to consider whether or not to place a stent in the case of the presence of stenoses impacting the coronary reserve, involves numerous steps to be implemented and generally requires an invasive intervention in the patient.

[0003] One of the most important constants in the evaluation and characterization of coronary flow is the coronary reserve called FFR and meaning in the English literature "Fractional Flow Reserve". Generally, the measurement of the FFR with the required precision is carried out from an invasive coronary angiography by the insertion of a catheter with a pressure sensor. Indeed, the FFR can be expressed as the ratio between two pressures measured upstream and downstream of a vessel by considering an upstream pressure measured at the level of the ostium in order to characterize the coronary flow of the vessel. Certain values ​​of the FFR can lead to patient monitoring, to one or more in-depth examinations, or even to an intervention for the placement of a stent.

[0004] Some solutions are based solely on an approach implementing a hemodynamic model of the vessels from the Navier Stokes equations. This is for example the case of the solutions described in application US2012 / 0041318 published on February 16, 2012. A problem with this approach is that such a system is complex to solve because it is a system of differential equations and the latter is solved in 3D. Such a system can involve significant computational resources. Finally, such a model does not take into account a customization of the coefficients of the system of differential equations, in particular the resistance coefficients, the compliance coefficients, and other boundary conditions.

[0005] Other solutions based solely on a machine learning approach do not allow optimal learning of a model to be trained. Indeed, such a model requires training on thousands, even millions of data due to the large number of numerical parameters measured in each patient corresponding to all the specifications of each patient and to all the flow configurations of the blood flows within each vessel. This is particularly the case of the application published under number FR3096498 and filed on 05 / 23 / 2019, with a model trained on 200 patients. However, the configurations can be very diverse depending on the type of vessel, the elasticity of the vessels, their length, the number of stenoses or other singularities present in the vessel, the flow rate, the age of the patient, etc.

[0006] Finally, an important constraint is that the collection of data during training requires measuring variables invasively and at different points of each vessel. Therefore, to date, there is no training of a machine learning model based on in vivo training data allowing the construction of a reliable model.

[0007] There is therefore a challenge in proposing a reliable, robust and non-invasive alternative to existing solutions. Summary of the invention

[0008] According to one aspect, the invention relates to a method for estimating the coronary reserve flow fraction of a vessel comprising: • Acquisition of at least one first image from an imaging system; • Extraction of a first set of data defining descriptors anatomical of a first vessel of said first image; • Acquisition of a second set of data, called patient data, including at least heart rate and myocardial mass; • Generating an input comprising the first data set, the second data set; • Generating an output defining a prediction of a coronary reserve flow fraction quantity by executing a first machine learning model to produce an output, said first machine learning model implementing a parameterizable loss function including at least a first factor modeling at least one parameterized physical constraint optimized during the training of said model, said parameterized physical constraint resulting in particular from a first numerical model of hemodynamic equations.

[0009] The method advantageously makes it possible to estimate the pressure at each point of the vessel and therefore makes it possible to estimate the fraction of the coronary reserve flow at each point of the vessel. One advantage is to have an estimate of the fraction of the coronary reserve flow that is precise and faithful to the specific case of the individual considered without using an invasive measurement. One advantage of using a cost function incorporating a physical constraint is to make the training of the machine learning model more efficient, in particular by using heterogeneous training data, i.e., data from different sources.

[0010] According to one embodiment, the extraction of the first set of data is obtained by means of a first segmentation of a representation of a set of vessels acquired by the imaging system, said extraction resulting from a selection of at least one first vessel displayed on a display, the selection of a point of the vessel.

[0011] One advantage is to make the most of the images acquired by an imaging system, in particular to extract anatomical data.

[0012] According to one embodiment, the anatomical descriptors are extracted from a representation of the first vessel, at least one first descriptor comprising data characteristic of the radius or diameter of the section in each position of the first vessel and at least one second descriptor comprising the positioning within the length of the vessel of at least one narrowing of the diameter defining the presence of at least one stenosis.

[0013] One advantage is to use personalized patient data to train the machine learning model and exploit the trained machine learning model.

[0014] According to one embodiment, the second descriptor comprises data characteristic of the inlet section of at least one portion defining the narrowing of the first vessel and data characteristic of the outlet section of at least one portion defining the narrowing of said first vessel.

[0015] According to one embodiment, the extracted anatomical descriptors also comprise: • A third descriptor corresponding to the local curvature of the vessel and / or • A fourth descriptor corresponding to the length of a stenosis and / or; • A fifth descriptor corresponding to a local dilation of the vessel (aneurysm).

[0016] An advantage is to allow certain parts of the vessel to be identified in order to characterize them and obtain a better estimate of the pressures thanks to the trained machine learning model.

[0017] According to one embodiment, the method comprises estimating the flow rate of the stream resting incoming blood flow rate from at least heart rate, systolic pressure and myocardial mass, the second data set comprising the value of said incoming blood flow rate.

[0018] An advantage is having measurable input data for each patient, the consideration of which allows a better estimation of the outlet pressure at each point of the first vessel.

[0019] According to one embodiment, the estimation of the flow rate of the incoming hyperemic flow at rest from at least the heart rate, the systolic pressure and the myocardial mass, the second set of data comprising the value of said flow rate of the incoming hyperemic flow.

[0020] An advantage is having measurable input data for each patient, the consideration of which allows a better estimation of the outlet pressure at each point of the first vessel.

[0021] According to one embodiment, the second set of patient data comprises in particular: • An Age of the individual; • A kind of individual; • An indicator of the individual's diabetes; • An indicator of the individual's hypertension.

[0022] An advantage is to have personalized input data, in particular from data that can be collected simply and which makes it possible to improve the prediction of the output pressure according to the patient profile.

[0023] According to one embodiment, the first machine learning model is a DeepONet network whose loss function integrates a second factor defining a loss function of a differential mathematical operator.

[0024] One advantage is to exploit a learning model without having to model and simulate a system of differential equations when using the data to estimate pressures within a first vessel.

[0025] According to one embodiment, the first factor is modeled during the training of the machine learning model by a parametric function whose parameters are dependent on the solutions of the equations of the numerical model of hemodynamic equations characterizing the hemodynamic flow in the first vessel, said parametric function being implemented by a continuous non-linear operator, the resolution of said parametric function making it possible to generate value limits outside of which the cost function is penalized.

[0026] An advantage is to obtain a more efficient function whose learning has made it possible to remove inconsistent values, for example violating physical laws.

[0027] According to one embodiment, the equations characterizing the hemodynamic flow in the first vessel to optimize the cost function and modeled by the first hemodynamic numerical model which includes a system of equations comprising: • A model of conservation of mass; • A model of conservation of momentum; • An equation of state for pressure.

[0028] An advantage is to take into account several constraints characterized by different physics equations and making it possible to limit the training domain.

[0029] According to one embodiment, the method comprises a training step carried out from a third set of training data characterizing portions of pipes each modeling an irregular geometry characteristic of at least one predefined section profile, the training of the machine learning model being supervised so that the values ​​characterizing the flow of a fluid in each portion are measured on a test bench comprising at least one portion of test pipe and sensors making it possible to measure test data at different points of said test bench including in particular the flow rate, the pressure, the viscosity, the resistance of the fluid, the Reynolds number and the density of the fluid.

[0030] An advantage of being able to generate numerous training data taking into account numerous anatomical geometries without requiring testing a wide variety of vessel geometries from different patients.

[0031] According to one embodiment, the method comprises a characterization of the different portions of the test bench, each portion being characterized by a radius of artery to be modeled, a length of artery to be modeled, an elasticity or a compliance and a type of portion.

[0032] According to one embodiment, the method comprises a pump, a clock and a means for recording a pumping frequency so as to inject a fluid into the test bench reproducing a periodic activity relating to the cardiac cycle characterizing the different portions of the test bench.

[0033] An advantage is that it allows a wide variety of parameters of the in vitro model to be controlled and different virtual patients representing a diversity of patients to be simulated.

[0034] According to one embodiment, the third data set also comprises a measurement and a calculation for at least one point of each predefined pipeline portion: • at least one output resistance modeling the force which opposes the flow of blood in the portion of the first vessel; • at least one impedance; • at least one fluid viscosity value; • at least one value of the equilibrium pressure.

[0035] An advantage is to allow the calibration of a test bench having characteristics similar to real vessel anatomical.

[0036] According to one embodiment, the method comprises a training step carried out from a second set of training data characterizing the geometry of portions of vessels obtained from an imaging system, the training of the machine learning model being supervised so that the values ​​characterizing the flow of a fluid in the first vessel are estimated by a second model of hemodynamic equations called a numerical solver, to define test and validation data for the machine learning model.

[0037] An advantage is to have a great possibility of training from medical data such as real images of patients of which the values ​​and the characteristics of the flow can be estimated to train the machine learning model of the invention.

[0038] According to one embodiment, a second segmentation of the first vessel automatically generates a plurality of segment types including: • a first type of segment defining substantially regular portions corresponding to portions of vessels having a section gradually decreasing from a proximal end towards a distal end; • a second type of segment defining at least one irregular portion, said at least one irregular portion corresponding to a portion comprising at least one narrowing of the diameter greater than a predefined threshold,

[0039] each of the sets of segments having a system of equations modeling the hemodynamic flow in said portion.

[0040] According to one embodiment, the second segmentation of the first vessel automatically generates a plurality of segment types including: • A third segment type characterized by the presence of a local curvature of the vessel greater than a predefined threshold and / or; • A fourth type segment characterized by local dilation of the vessel (aneurysm). • An advantage is to model the flow as close as possible to the reality of the flow in each portion taking into account the anatomy of the vessel considered.

[0041] According to one embodiment, the numerical solver comprises a system of equations characterizing the physics of the flow of a hemodynamic flow from the incompressible Navier Stokes equations applied to at least one portion of a single-dimensional vessel.

[0042] One advantage is to simplify the equations and allow easier training. by reducing the dimension of the solver.

[0043] According to one embodiment, the system of equations comprises a second hemodynamic digital model comprising for each portion of vessel at least one model among which: • A model of conservation of mass and / or; • A model of conservation of momentum and / or; • An equation of state of pressure and / or; • A first model of a pressure delta and / or; • A second model of a pressure delta established from the in-vitro measurements.

[0044] According to one embodiment, the method comprises a calculation of the blood flow characteristics in each portion of the first vessel at each point of the axis of the vessel from the second hemodynamic model applied locally to each of the portions.

[0045] According to one embodiment, the second hemodynamic digital model makes it possible to estimate for each portion of vessel of the second type a pressure delta from a pressure delta model comprising a viscous resistance coefficient and a turbulent resistance coefficient.

[0046] One advantage is having a semi-empirical model that can be refined for each anatomical profile considered.

[0047] According to one embodiment, the second hemodynamic digital model makes it possible to estimate for each portion of vessel of the second type, of the third type, and / or of the fourth type a pressure delta from a pressure delta model comprising a viscous resistance coefficient and a turbulent resistance coefficient, said coefficients being estimated from tests carried out on an in vitro test bench of the invention, said measurements carried out on the test bench making it possible to estimate flow characteristics of a fluid.

[0048] An advantage is to use in vitro measurements to obtain a model of equations as close as possible to the anatomy of the portion of vessel considered.

[0049] According to one embodiment, the first machine learning model is trained by considering the values ​​estimated by the second model integrated over the entire first vessel.

[0050] One advantage is to simplify the use of the machine learning model by exploiting only a limited number of input data.

[0051] According to one embodiment, a first set of training data comprises geometry data extracted from a patient vessel imaging system, patient data comprising at least the heart rate, the systolic pressure and the mass of the myocardium and test and validation data from pressure measurements at different points of the vessel portion.

[0052] considered. According to another aspect the invention relates to a method of training a machine learning algorithm to produce a trained network for calculating the pressure of a fluid at a plurality of positions within a first vessel as a function of time within the cardiac cycle, said training method comprising: • Acquisition of a first set of training data from: • Acquisition of a first image from an imaging system; • Extraction of a first set of data defining anatomical descriptors of a first vessel of said first image; • Acquisition of a third set of data, called patient data, including at least heart rate and myocardial mass; • Reading data characterizing pressure measurement points of a first vessel defining test and validation data for a machine learning model; • Execution of the machine learning model and learning by implementing a cost function minimizing the error between data produced by the model and the test and validation data; • Acquisition of a second set of training data from: • Acquisition of a first image from an imaging system; • Extraction of a first set of data defining anatomical descriptors of a first vessel of said first image; • Resolution of a solver modeling a hemodynamic equation model from the incompressible Navier Stokes equations in one dimension, the data estimated by the solver defining test and validation data for a machine learning model; • Execution of the machine learning model and learning by implementing a cost function minimizing the error between data produced by the model and the test and validation data; • Acquisition of a third set of training data from: • Modeling of a set of geometries defining pipes suitable for conveying a fluid whose viscosity is substantially that of blood and suitable for being arranged within a test bench; • Performing a set of fluid flow tests with a variety of different geometries within the test bench; • Measurement of data characterizing pressure measurement points of a first portion of channel defining test and validation data for a machine learning model; • Execution of the machine learning model and learning by implementing a cost function minimizing the error between data produced by the model and the test and validation data.

[0053] One advantage is having a wide variety of training data to train the model on a wide variety of cases. Another advantage is that the different branches or training data can be used to configure another branch. Thus, in vitro data can be used to parameterize the training branch based on the CFD solver. Similarly, data acquired by imaging real patients can be used to parameterize the CFD solver. Brief description of the figures

[0054] Other characteristics and advantages of the invention will emerge on reading the detailed description which follows, with reference to the appended figures, which illustrate: • [Fig.l]: a representation of the different systems making it possible to acquire and process the data and images of a patient's vessels to predict the FFR of at least a first vessel; • [Fig.2]: a representation of the result of a segmentation step of a 3D artery with multiple vessels with the creation of central lines for each arterial vessel; • [Fig.3]: a representation of a particular vessel for which we wish to estimate the FFR from a segmentation according to an embodiment of the method of the invention; • [Fig.4]: a representation of a vessel straightened along an Ox axis allowing to implement a segmentation step of an embodiment of the method of the invention; • [Fig.5]: an embodiment of the main steps of the FFR estimation process; • [Fig.6]: an embodiment of the main steps of the method for training a machine learning model according to the invention; • [Fig.7A]: an example of the implementation of an architecture at one output of a DeepONet type network comprising the implementation of a cost function parameterized according to physical constraints; • [Fig.7B]: an example of the implementation of a multi-output architecture of a DeepONet type network including the implementation of a cost function parameterized according to physical constraints; • [Fig.7C]: an example of an embodiment of an architecture of [Fig.7B] implemented according to the methods of the invention; • [Fig.8]: an example of a test bench allowing measurements to be taken to define a training data set containing data to test and validate the machine learning model; • [Fig.9]: an example of a geometry model that can be used on the bench test of [Fig.8]; • [Fig. 10]: other examples of geometry model of a stenosed portion that can be used on the test bench of [Fig.8], • [Fig.l 1]: an example of second adapted segmentation implemented to cut different vessels according to segment types. Definitions

[0055] In the present invention, the term "FFR" refers to a ratio between an inlet pressure of a vessel and an outlet pressure.

[0056] We call “Pa”: the inlet pressure of a vessel.

[0057] We call “Pd”: the outlet pressure of a vessel.

[0058] We call “Pdi”: the pressure along the axis of a vessel.

[0059] ON calls "ST": a stenosis in the general case and "ST;" when a stenosis in particular is designated is described in an example.

[0060] A “DON” network is called a DeepONet network, which in English means “Deep Operator Network”.

[0061] A machine learning model trained to generate outputs from input data is called “MLAi”.

[0062] We call “ENS / ”, “ENS / '”, “ENS / "” the data necessary for training the machine learning model used according to different data sources.

[0063] ENS / refers to training data used and measured in vivo.

[0064] ENS / ' refers to training data obtained from a model mo unraveling the hemodynamic flows M0D2.

[0065] ENS / ” refers to training data used and measured in vitro.

[0066] The data acquired by the machine learning model is called “ENSi” when operating the trained model. Note that the data in the ENSi set may include additional data with respect to one of the ENSi ' or ENS / ' sets, in particular “patient data”.

[0067] We call “ENS2” the “patient data” corresponding to the measured physiological data, demographic data, history, etc., this data end up being part of the input data of the trained MLAi machine learning model.

[0068] We call “ENS2'” the “patient data” to train the MLAi machine learning model corresponding to the measured physiological data, demographic data, and history.

[0069] It is possible in certain embodiments that the ENS2 data is used for training the MLAi model, consequently, data from the ENS2 set may be included in the ENS2' set.

[0070] The term "CFD" refers to a solver of Navier Stokes differential equations, which in English means "computational Fluid Dynamics" meaning numerical analysis of fluid mechanics.

[0071] A solver of Navier Stokes differential equations in one dimension is called "1-D CFD".

[0072] We call Lopé(0): the term or factor of a cost function modeling the loss to be minimized of an operator model of a network integrating in-vivo and in-vitro physiological training data. It is also noted LoperatOr(0)-

[0073] We call Lphy(0): the term or factor of a cost function modeling the loss to be minimized in a system of physical equations of a network integrating physical constraints. It is also noted Lphysics(0).

[0074] A “first segmentation” SEGi is called the segmentation making it possible to acquire images from a 3D imaging system and to select a vessel or artery of interest and to calculate the interior and exterior volumes and to calculate the central lines of the vessels or arteries.

[0075] A “second segmentation” SEG2 is called the segmentation allowing a vessel to be cut into several longitudinal portions in order to use a hemodynamic equation model M0D2 to model the blood flow in each of the portions.

[0076] The term "HIS" refers to the hospital information system, the acronym for "Hospital Information System" in English. It can also correspond to the system for managing electronic patient health records.

[0077] The name “CFS” refers to the cardiac analysis system, the acronym of which stands for “Coronary Flow System” in English terminology.

[0078] Resistance is generally denoted R or R2 in the equations. Resistance refers to the force that opposes the flow of blood through the blood vessel. It is influenced in particular by the diameter and length of the vessel, the viscosity of the blood, the type of flow: laminar or turbulent, and the elasticity of the vessel walls.

[0079] Impedance is generally denoted Zc and Ri in the equations. Impedance allows for the dynamic aspects of flow and vessel to be taken into account, particularly as the vessel contracts and expands over time within the cardiac cycle. Impedance can also reflect the influence of pressure waves and the frequency dependence related to heart rate.

[0080] Compliance is denoted C, it can be expressed as the inverse of elasticity. Elasticity can also be called elastance. It corresponds to the capacity of a tissue to return to its initial state after undergoing deformation. Compliance refers to the capacity of a vessel to dilate and increase in volume in response to an increase in internal pressure.

[0081] The values ​​Po, Ao correspond to values ​​measured or estimated or calculated at equilibrium. It corresponds in the cardiac cycle to the instant in which the fluid, that is to say the blood, is least subject to dynamics. This corresponds for example to a local minimum of certain values ​​in dynamics, in particular the speed or the flow rate.

[0082] The method applies equally to vessels and arteries. Thus, in the present invention, when the vessel 10 is designated, the described embodiments also apply in the same way to an artery.

[0083] The invention relates on the one hand to a method for predicting the pressure and a value of the FFR of a vessel of the myocardium of an individual from a trained machine learning model and a method for training said machine learning model making it possible to predict the FFR of a vessel of the myocardium of an individual. The invention can relate to any type of vessel other than those of the myocardium for which an expression of the flow rate or an incoming flow of blood is available as input. In the latter case, the “in vivo” training branch is then adapted according to the type of vessel considered and therefore the associated trained machine learning model. Method for predicting FFR

[0084] The method for predicting FFR involves several steps.

[0085] [Fig.5] represents an embodiment of the steps of the method for estimating the FFR. Image acquisition

[0086] According to one embodiment, a first step comprises an acquisition of at least one image of a set of at least one vessel from an imaging system. According to one embodiment, a plurality of images is acquired so as to reconstruct a complete 3D image of a region of interest. The imaging system may be a scanner such as a coronary CT scanner, an MRI or an ultrasound imaging device. These images are called DICOM images and designate in the English terminology "Digital Imaging and Communications in Medicine". A This format allows for image interoperability with different systems. In addition, different data can be associated and saved with the image, including patient data. In addition, the format allows the use of imaging data to perform operations and display certain parameters.

[0087] This step is noted ACQi in [Fig.5]. The corresponding step during the training phase is noted ACQi in [Fig.6].

[0088] According to one embodiment, a coronary CT scanner is implemented to collect images of an individual. Such an imaging system is based on a medical computed tomography imaging system. It is also called a coronary CT angiography and noted in the literature CTCA designating "Coronary Computed Tomography An-giography" in English terminology. The image produced is obtained using an X-ray device. The data collected is then processed by a computer to create cross-sectional images of the heart. These images can be compiled to form a 3D view of the coronary arteries as shown in [Fig.2]. The method of the invention makes it possible to recover clear images of the heart and arteries.

[0089] An advantage of this imaging system is that CTCA is non-invasive, fast, and provides high-resolution images, allowing detailed evaluation of the coronary arteries.

[0090] [Fig.l] represents different components of a non-invasive imaging system such as a CTCA.

[0091] [Fig.l] represents a first block denoted HIS allowing the collection of data measured in a patient by measuring devices such as imaging data like an MRI image or an image from a Coroscanner. This component is also capable of receiving reports or analyses produced by the CFS component.

[0092] A second block, called PACS, allows the acquired medical data to be archived, recorded and transmitted. The PACS component includes a data server.

[0093] A third block noted VIEW allows you to view the acquired images, to create the first segmentation and to use metadata and data from the first SEGi segmentation.

[0094] A fourth block denoted CFS comprises a calculation unit making it possible to use the first segmentation SEGi as input and to carry out the second segmentation SEG2 of said images if necessary during the training of the machine learning model MLAi or during the exploitation of the CFD model M0D2.

[0095] According to one embodiment, this calculation unit is also used to implement the CFD solver and / or the MLAi model for the calculation of the FFR.

[0096] According to one embodiment, this calculation unit is configured to generate a “report” type report allowing to restore the main outputs of the MLAi model, the acquisition data and the data calculated from the data produced by the MLAi model. This report can be displayed on a computer display so that an operator or a doctor can consult it.

[0097] [Fig.2] represents a segmented 3D view of the aorta 11 and the coronary vessels (eg LAD, LCX, RCA). A vessel 10 is represented among other vessels. It is subsequently called “first vessel” and is noted 10. The method of the invention makes it possible to select a vessel for which the FFR is to be estimated, such as the first vessel 10, from the method of the invention.

[0098] [Fig. 3] represents the first vessel 10 whose image was acquired using an imaging system such as a corona scanner and which was selected from a selection operation carried out on the display.

[0099] According to another embodiment, the method automatically triggers the method of the invention on all of the acquired vessels or a pre-selection of a subset of identified vessels.

[0100] In the remainder of the description, the method applies to the analysis of a vessel 10 selected from a display.

[0101] [Fig.3] in this case represents a 2D sectional view of a vessel 10.

[0102] In the case of [Fig.3], the first vessel 10 comprises different stenosed STb ST2 or non-stenosed 6 portions which can be selected using a selector or a method of automatic detection of diameter variations. Representation of images

[0103] The method of the invention comprises processing the images of the first vessel 10 so as to enable its display from a CFS display. To this end, an image recognition algorithm is implemented in order to isolate certain parts of interest and to segment the image.

[0104] The method of the invention makes it possible to generate a two-dimensional representation of a vessel. The represented vessel is advantageously selected beforehand from a selector. An operator can select an artery, an opening vessel or a portion of a vessel from the operating system of the acquired images. For this purpose, an image processing algorithm can be implemented so as to automatically crop the images and extract the pixels of at least one vessel or artery within an image to display a representation thereof.

[0105] [Fig.2] illustrates the result of the first segmentation with the creation of the central lines for each arterial vessel. This step is implemented at the VIEW step of [Fig.l].

[0106] A first SEGi segmentation makes it possible to collect the images from the imaging system and to select the pixels of interest of a vessel or more generally of an organ.

[0107] A segmentation algorithm makes it possible to analyze the spectral densities of the acquired image, the contours of shapes and contrasts of the latter according to the imaging system used in order to exploit the portions of interest of an acquired image.

[0108] This first SEGi segmentation makes it possible to select a vessel, for example, by selecting a group of pixels of interest from an area to be retained. When analyzing a shape defining a vessel, a proximal reference point and a distal reference point are automatically calculated in order to select a longitudinal portion of a vessel.

[0109] According to one embodiment, a proximal reference point is defined with a parent artery. The distal reference point may correspond to a point in an area in which an anatomical reference can be taken, or a given diameter of a point located below a predefined diameter. This predefined diameter corresponds for example to a value of 1.5 mm. This limit corresponds to the current resolution limits of coronary CT scanners. However, if this limit were to decrease or if another more efficient imaging system were to be used, the invention could be applied to a vessel up to a distal end having a radius less than 1.5 mm in order to adjust a new distal reference.

[0110] The first SEGi segmentation makes it possible to delimit the external surface of the vessel and the internal surface of the vessel and to calculate an average central line of the vessel.

[0111] According to one embodiment, the method of the invention comprises the implementation of a rectification algorithm making it possible to generate a display of the vessel in a 2D representation along an axis Ox which can define for example the central line of the vessel.

[0112] The first SEGi segmentation includes the possibility of defining a marker along the vessel on the 2D representation or the 3D representation so as to visualize section planes of the vessel. For this purpose, a selector allows a user to select a section plane from a marker.

[0113] According to one embodiment, the first SEGi segmentation makes it possible to delimit portions of all or part of a vessel or an artery in order to select said portion and mark said portion in order to annotate the representation. One advantage is to make it possible to annotate portions of metadata that can be used during the training of the MLAi machine learning model or during the exploitation of the CFD M0D2 model called CFD. Representation of the selected vessel

[0114] [Fig.4] illustrates a representation of a vessel 10 straightened along an axis Ox. The figure represents different parts of the vessel 10 and different descriptors of the ship 10.

[0115] An advantage of this representation is that the diameter or the internal radius of a portion of vessel or artery comprising at least one stenosis can also be visualized along the same longitudinal axis and therefore according to a common reference of all the diameters of said vessel or said artery.

[0116] Within [Fig.4] are represented plaques denoted 4 such as calcium plaques in this example which form on the inner wall of a vessel 10. The stenoses are detected using imaging, they correspond to local reductions in diameters or radii of the first vessel 10.

[0117] Preprocessing and extraction of anatomical features

[0118] Anatomical data is used to define part of the input data of the MLAi machine learning model and is also used for training the MLAb model

[0119] According to one embodiment, the input data of the trained model comprises a first set of ENSi data characterizing the anatomy of at least one vessel from an acquired image of the individual. The method makes it possible to select a first vessel 10 from an acquired image and to automatically extract from a processing of the image data characterizing each portion 6, ST of the first vessel 10.

[0120] The extraction step is noted EXTi in [Fig.5] illustrating the implementation of the method for estimating the FFR. The corresponding step during training is also noted EXTi in [Fig.6].

[0121] The internal diameter is preferentially extracted over the entire length of the first vessel 10 by means of an analysis and processing of the acquired images. - Curvature

[0122] According to one embodiment, the method comprises a step of calculating the curvature of the vessel at different points of the vessel. According to one embodiment, a function Cb(x) defines the function making it possible to determine the curvature as a function of the position x on the longitudinal axis Ox of the representation of the straightened vessel of [Fig.4] or of the central axis of the non-straightened vessel.

[0123] The curvature of the vessel can therefore be recorded during this operation so as to be reused subsequently as data to model certain portions of the vessel, for example during the training phase using a hemodynamic model M0D2. The method makes it possible to annotate the portions having a curvature greater than a given threshold, for example in the second segmentation step SEG2.

[0124] This operation is carried out in particular during the second segmentation SEG2. Indeed, when the curvature is greater than a given threshold on a portion of the vessel, the hemodynamic flow in these portions can be modeled by one or more dedicated equation(s).

[0125] According to one embodiment, the curvature of certain portions of the vessel can be used as input to the MLAh machine learning model.

[0126] The method of the invention makes it possible to index along a vessel 10 considered all of the radii or internal diameters along said vessel 10. According to an improved mode, the external radius can be measured and indexed along the vessel 10 considered. One advantage is to consider the thickness of the wall of a vessel 10. However, the invention can be implemented without consideration of the thickness of the vessel or artery considered.

[0127] During the image processing operation, a function of the radius r(x) can be generated by taking all the radii of the vessel or artery considered from an origin position x0 to a terminal position xt. The sampling resolution of the function can be defined so as to discretize all the values ​​on a predefined scale.

[0128] According to one embodiment, all of the curvatures of the vessel 10 are also indexed along the straightened vessel along the longitudinal axis Ox. Thus, the method of the invention makes it possible to collect, by automatic analysis of the image, all of the values ​​of radii or internal diameters and all of the values ​​of curvatures of the vessel 10 considered. These values ​​are recorded in a memory and each of the values ​​is associated with a position of the vessel 10 along the longitudinal axis of straightening. - Singularity

[0129] The method of the invention comprises a step of detecting a set of singularities along the vessel 10 considered.

[0130] According to a first example, a first type of singularity is a plaque 4. According to a second example, a second type of singularity is a junction zone or a bifurcation zone. According to a third example, a third type of singularity is an aneurysm. Other types of singularities can be noted.

[0131] In the remainder of the description, the case where plaques 4 cause the formation of a stenosis or several ST stenoses will be considered as an example. - Stenosis

[0132] [Fig.4] represents an example case in which two stenoses STi and ST2 are identified using image processing. Automatic detection of stenoses can be configured by automatic analysis of the variation of the diameters or internal radii of the vessel over the entire portion analyzed. It is noted that [Fig.4] represents plates 4 not managing stenoses and others resulting in the formation of STi and ST2 stenoses. The method of the invention allows to identify and annotate the presence of stenoses on an image of a vessel.

[0133] According to one embodiment, direct identification of stenoses is not provided and autoencoders are used. Autoencoders are a type of neural network used in machine learning for unsupervised learning. They consist of an encoder and a decoder, and their objective is to learn a latent representation of the input data. The latent representation is provided with additional necessary properties and can be used, for example, to reduce the dimensionality of the data or to eliminate noise. The invention includes other implementations of autoencoders for 2D and 3D input data.

[0134] The presence of an ST stenosis is the consequence of a local reduction in the radius or the internal diameter of the first vessel 10. Each ST stenosis can be detected and identified using an image analysis algorithm. Different existing algorithms can be applied within the framework of the present invention, such as the autoencoders previously mentioned. The detection of stenoses allows them to be counted along the first vessel 10. The vessel portions comprising an ST stenosis are indexed and the presence of said ST stenosis can be characterized by a set of positions xs along the Ox axis. The stenoses in [Fig.4] are denoted ST! and ST2.

[0135] Each ST stenosis can be characterized according to different criteria. A first criterion corresponds to its dimensions. The dimensions of an ST stenosis include at least the length along the Ox axis and the thickness along the axis perpendicular to the Ox axis of the ST stenosis. The occlusion diameter or the minimum radius in the stenosed portion can be extracted.

[0136] According to other embodiments, the following parameters can be used to characterize a stenosis: - The minimum diameter of the stenosis in mm and / or; - The minimum area of ​​the stenosis in mm2 according to a section plane of the vessel and / or; - The total volume of the stenosis in mm3 and / or; - The maximum degree of coronary stenosis expressed as a percentage of vessel diameter and / or; - The maximum degree of coronary stenosis expressed as a percentage of the vessel surface area according to a sectional plane of the vessel and / or; - The curvature of the area corresponding to the stenosis.

[0137] These morphological parameters are for example calculated from the identified singularity such as a plate-type singularity.

[0138] According to one embodiment, the diameter or the inner radius of the vessel 10 at each position of a stenosed portion STb ST2 can also be calculated. This the latter data can supplement, for example, data characterizing the thickness of the stenosis in the method of the invention.

[0139] In the case of [Fig.4], two STb ST2 stenoses were identified along vessel 10. A first stenosis has a length LSTi the second stenosis has a length LST2- The radius or diameter in these portions can be noted.

[0140] According to one embodiment, the distance between two stenoses STi and ST2 can also be taken into account by a measurement on the image. The measurement can advantageously be carried out automatically from an image processing algorithm. This data can be used for training and / or exploitation of the trained MLAh model.

[0141] According to one embodiment, the vessel can be divided into several segments in order to calculate the inlet pressure and the outlet pressure of each segment, in particular during the second segmentation to train the model.

[0142] We consider the case in the remainder of the description where a vessel is considered entirely from an entry point, generally a junction zone with an artery and a distal end defined by a geometric or anatomical marker.

[0143] [Fig.4] is used to describe a vessel used during the exploitation phase of the MLAi model and also to describe a vessel used during the training phase for example from a M0D2 hemodynamic model for which one equation can be associated with non-stenosed portions and another equation can be associated with stenosed portions.

[0144] The pressure curve makes it possible to visualize the evolution of the pressure along the vessel. This curve, although represented in [Fig.4], cannot be obtained directly from the imaging. The method of the invention makes it possible to overcome this problem since the objective of the invention is to predict the pressure values ​​along the vessel 10 from a trained MLAi machine learning model.

[0145] When the pressure points are obtained, it is possible to consider two points at the entrance and exit of the vessel 10 to calculate the FFR.

[0146] The method of the invention makes it possible to estimate, as shown in [Fig.4], the pressure p(x) at any point of the vessel. In this case the FFR is then calculated in a second step from the predicted values ​​of the pressure Pd and Pa.

[0147] According to one embodiment, the predicted value is a value of the FFR which is a ratio between an inlet pressure Pa of a vessel and a pressure at a considered point of the vessel, for example the outlet pressure Pd. We have the following relationship which is verified at any point x of the vessel: FFR(x) = P(x) / Pa.

[0148] The pressure estimation can also be done using the second CFD model called M0D2 in order to train the MLAi model with the values ​​estimated by the solver.

[0149] This representation makes it possible to illustrate the pressure drops after the presence of a stenosis.

[0150] During the training step using the training data, a pressure curve can be obtained along the Ox axis of the vessel in which a catheter equipped with a pressure probe navigates. The invention can use such data made available and recorded in a memory.

[0151] The input of the MLAi machine learning model corresponds to the entire vessel or artery considered such as that represented in [Fig.4]. The artery or vessel is a topological unit, going from the input to the output. In the case where there are several branches in the artery, for example an LDA and LCX branch or an RCA branch, the MLAi model considers each of them independently. An exchange of data such as the extractions of anatomical characteristics, the flow q or the pressure p at the junction zones makes it possible to take into account the different junction constraints.

[0152] According to one embodiment, the length of the vessel 10 from a characteristic entry point to a characteristic exit point may also define an input data of the MLAp machine learning model. The characteristic points may correspond to bifurcation points, to a point of the vessel corresponding to a narrowing of the diameter greater than a threshold, etc. Process input data for predicting FFR

[0153] The anatomical data defined previously defines a part of the input data, noted ENSb of the MLAb machine learning model

[0154] According to one embodiment, the input data of the trained MLAi model comprises a second set of ENS2 data characterizing the individual. Input flow rate

[0155] According to one embodiment, the resting input flow rate Qrest is calculated from the mass of the myocardium Mc which is data acquired at the input of the system. An algebraic model makes it possible to express the resting input flow rate Qrest from the mass of the myocardium Mc.

[0156] According to one embodiment, the input data of the MLAi model is the mass of the myocardium Mc or the mass supplied by one of the vessels, or the mass of a part of the myocardium such as the mass of a left ventricle, MC LV.

[0157] According to another embodiment, the input data of the MLAi model is a flow rate calculated from the mass of the myocardium Mc or from the mass of a part of the myocardium.

[0158] In the latter case, the method comprises a calculation of the resting flow rate in the first vessel 10 whose myocardial mass Mc is known.

[0159] Depending on the vessel selection, the fraction of blood in the artery supplying said vessel is considered.

[0160] The method of the invention makes it possible to deduce from the selection of the first vessel 10 considered the upstream flow rate supplying said first vessel 10. There are three main arteries supplying the heart and therefore all the vessels. The 3 arteries are denoted LAD, LCX and RCA.

[0161] The first artery LAD designates the artery called "Left Anterior Descending artery" in Anglo-Saxon terminology and in French: "The anterior interventricular artery". This artery supplies the anterior part of the heart, in particular the left ventricle.

[0162] The second artery LCX refers to the artery called "Left Circumflex" in Anglo-Saxon terminology, or in French the left circumflex artery. It supplies blood to the lateral wall of the heart, mainly to the left ventricle.

[0163] The third RCA artery refers to the "Right Coronary Artery", or the right coronary artery. It mainly supplies the right ventricle and part of the left ventricle.

[0164] These arteries supply oxygenated blood to the different parts of the myocardium. The blood flow in these arteries can be calculated according to known proportions of blood ejection in each artery.

[0165] A relationship allows the resting flow rate in a given vessel to be deduced.

[0166] According to one embodiment, the following relationship can be written:

[0167] Qrest = 2.5 * (Mc075) [ml / min],

[0168] According to another embodiment, if only the mass of the left ventricle MC LV is known, this relationship can be written:

[0169] Qrest_LV =12*((0.7*( fc * Psyst) / 1000)-0.4) * MC_LV / 100 [ml / min],

[0170] where fc is the heart rate and Psystest the systolic pressure. This relationship is only valid if the flow rate meets the individual's oxygen demand.

[0171] In the case of characterization of a hyperemic flow, a hyperemic flow coefficient khyp can be calculated according to an empirical formula.

[0172] khyp = 4.5 - 0.018 * ds + 0.00056 * ds2 - 0.0000085 * ds3

[0173] with ds: The maximum degree of coronary stenosis expressed as a percentage of vessel diameter.

[0174] The following relationship can be written: Qhyp = Qrest * khyp

[0175] If only the mass of the left ventricle is known, the relationship can be written as Qhyp = Q * r rest_LV Nivp

[0176] According to one embodiment, the model includes as input only the mass of the myocardium Mc. According to another embodiment, the model includes as input the mass of the myocardium and the resting flow rate as input. It is understood that the two inputs Q rest and Mc are strongly correlated and therefore that a single value can be considered in MLAb model input However, the model can consider both inputs. Patient data

[0177] These data are noted ENS2 in [Fig.5] and ENS2' in [Fig.6] for the “in vivo” training data. According to one embodiment, the heart rate of the individual is the input to the MLAi model.

[0178] According to one embodiment, additional data is taken into account with the value of the individual's systolic pressure.

[0179] According to one embodiment, the age of the individual is an input to the MLAi model. According to one embodiment, the gender of the individual is also an input to the MLAi model.

[0180] According to one embodiment, the weight and height of the individual are inputs to the MLAi model.

[0181] According to one embodiment, background data are inputs to the MLAi model such as the presence of diabetes, hypertension, the existence and count of previous percutaneous coronary intervention(s), the existence and count of myocardial infarction, the quantification of tobacco consumption. Contextual data Standardization

[0182] The method for estimating the FFR of the invention comprises a step aimed at normalizing NM the data forming the anatomical descriptors extracted from the segments / portions of the first vessel 10 and at normalizing the patient data. This step is noted NML in [Fig.5] and in [Fig.6]. The normalization step is therefore designated NML in training or in exploitation of the machine learning model MLAh. The normalization steps are by construction designed to generate normalized outputs whatever the training data. Thus, only the input data can possibly change at the input of the NML blocks.

[0183] The input data may have different formats depending on the data collected. The NML normalization block therefore allows potentially different transformations to be applied to the measured values.

[0184] According to one embodiment, the NML normalization comprises a step of scaling the values ​​according to a predefined scale. The NML normalization also comprises a transformation of the data according to a predefined system of units.

[0185] According to another embodiment, the NML normalization step comprises an upgrade of the precision of the data and its format. The NML normalization makes it possible to generate the data format making it possible to process the input vector in the same way as the input vector was used for training according to the different training branches.

[0186] According to one embodiment, a data imputation technique is applied to the input data to fill in missing values.

[0187] The input of the MLAi machine learning model is denoted Ei in [Fig.5].

[0188] The corresponding inputs on [Fig.6] during the training phases are noted ENS / , ENSi”, ENSi”', ENS2'. The test and validation data E2, E3, E4 allow the model to be trained by correcting the error of a cost function Lf. MLA Model Release

[0189] The method of the invention implements an MLAi machine learning model to produce output data denoted Si in [Fig.5]. In particular, the output data includes the predicted values ​​of pressure along the vessel, of the flow rate along the vessel, and of the values ​​of the sections of the vessel 10.

[0190] The predicted pressures are used to derive the FFR function along the axis.

[0191] The corresponding outputs during training are noted respectively S2, S3 and S4 according to the training branches of [Fig.6].

[0192] Among the data produced by the MLAi model, it is possible to exploit the inlet pressure Pa considered at the cutting plane defining the inlet of the vessel and the pressure Pd considered at the cutting plane defining the outlet of the vessel.

[0193] From the pressures produced by the MLAi model, the method of the invention comprises a step of calculating the FFR, namely the Pd / Pa ratio. This step is represented in [Fig.5] illustrating the method for estimating the FFR or the output pressures. This step is also represented in [Fig.6] representing the training method.

[0194] According to one embodiment, the flow rate Q is predicted by the MLAi model at any point x of the vessel and throughout the cardiac cycle, including as a function of time t.

[0195] Finally, the values ​​of the input and output sections A can be generated and the evolution of this section A(t) during the cardiac cycle can also be calculated by the MLAi model. Finally, the model can be trained to produce the equilibrium section Ao.

[0196] According to one embodiment, the method of the invention comprises a step of processing the data generated by the MLAi model to produce new values ​​of parameters of interest.

[0197] According to an embodiment corresponding to that of [Fig.7C], the values ​​of interest are the equilibrium pressure Po, the resistance R and the compliance C and the impedance Zc at the output of the portion considered, i.e. calculated at the output section plane. In [Fig.4], this output section plane is the plane pc6. In [Fig.1 1], this section plane can be defined at the point(s) OBi, OB2, OB3 or OB4. Model

[0198] The invention implements a model for predicting pressure and other factors associated characteristics of a vessel, taking into account various geometric and physical constraints. The model is based on scientific machine learning (SciML), a research field that uses deep learning to solve complex physical problems. An example of a SciML model is the physics-based neural network (PINN). Such a network is particularly suited to learning physical laws, particularly nonlinear ones, for example, approximated by differential equations. One advantage of such a network is that it allows working on physical processes in stenosed vessels. However, PINN can only provide solutions for defined vascular parameters, such as the geometry of the vessel or the position of the stenosis. The inclusion of each new parameter value requires a separate simulation, involving a complete retraining of the PINN.To overcome these limitations, one embodiment uses a physics-based DeepONet type network also denoted . “PIDeepONet”. Such a network is referred to as an MLAi model in this application. The PIDeepONet network can be used to learn various linear or nonlinear operators and impose physical constraints. DeepONet Network

[0199] According to one embodiment, the method of the invention implements an MLAi machine learning algorithm based on a DeepONet network, denoted DON. Such a network is designed to learn mathematical operators. In this context, such an operator is a function called "mapping" in English terminology. It transforms one function into another. The DeepONet network learns this transformation directly from ENSi' training data.

[0200] In a DON type network, the loss function Lf is designed to capture the error between the network predicted outputs and the actual or expected outputs for a given set of input functions. The general form of the loss function in a DON is typically a function of the error between the network prediction and the true output for various input samples ENSI', ENS2', ENSI”, ENSi'”.

[0201] In the case of a network trained to learn a mathematical operator, the loss function may include terms that evaluate the accuracy with which the derivatives are predicted.

[0202] In order to represent the mathematical operator from the data, the DON network makes it possible to consider two components generally noted "trunk" and "branch" in English terminology. The "trunk" component or branch is noted Bt and the "branch" component or branch is noted Bb in the rest of the description.

[0203] [Fig.7A] represents an architecture of a network called in Anglo-Saxon terminology “Physics informed DeepONet”. This example of DON type architecture is advantageously carried out in the method of the invention.

[0204] A physics-informed DeepONet network allows output functions to be consistent with physical constraints by minimizing loss taking into account underlying physical laws.

[0205] This architecture includes inputs {u(xi)]i and {yk(i)}k defining the inputs respectively of two branches Bb and Bt of the network.

[0206] [Fig.7A] represents an example of a single-output architecture.

[0207] According to one embodiment, the methods of the invention implement a multi-output network architecture. [Fig.7B] represents an example of a multi-output architecture. In this example, the outputs of branch Bb of the network are divided into n groups and the outputs of branch Bt of the network are also divided into n groups. Then the kth output of each group are processed together and produce the kth solution.

[0208] [Fig.7C] represents an example of an architecture with n outputs used in the context of the invention so as to generate different outputs here represented by the pressure P, the flow rate Q, the section A and the section Ao at equilibrium. In this figure, the secondary outputs are represented. The secondary outputs are the data calculated in a second step from the data produced by the MLAp network. They are therefore obtained indirectly. [Fig.7C] represents in particular the FFR obtained along the axis of the vessel, the pressure at equilibrium Po, the impedance Zc, the compliance C and the resistance R.

[0209] The model can be expressed as a function G(u)(y) taking as inputs of the model the two inputs {u(xi)]i and {yk]k to generate a prediction. / >|Math 1] Gg "OOCy) = / 1 I MazX - > M*m)) My) + ? I \ teafich Suais /

[0210] Where i=l, ..., K

[0211] WhereO = po <pi < ... <pn

[0212] The inputs {u(x;)}iEli ;NJ represent N distinct input functions. And for each yk(i) taken on an interval K e [1 ; P], there are P values ​​taken in the domain of the function G(u(i)). The generated output is denoted G(u(i),y(i)).

[0213] In the case of the present invention, the values ​​yk(i) are the input data received and processed as input to the MLAi model for each input sample. A sample comprises all the input data of an individual such as his age, heart rate fc, myocardial mass Mc, etc. A sample can also correspond in the case of training the model to a sample of a case modeled in vitro or simulated from a CFD model to which data from fictitious / virtual patients have been assigned.

[0214] u(Xi) is a function restoring the parameters making it possible to describe the different anatomies of vessels or portions of vessels defining the anatomical input data for ENS / training. u(xi) is a function making it possible to process the ENS / training data in order to train the MLAb model

[0215] u(Xi) corresponds to the input functions, which describe the geometric / anatomical characteristics of the vessel in the sensor points x. In one embodiment, u(x) is defined in the domain [0, 1] and depends on the distance to the stenosis. For such functions, 0 corresponds to 100% stenosis and 1 means no stenosis. In another embodiment, the functions u(x) are determined by an internal representation generated by the autoencoder network. In this case, the construction of u(x) is an unsupervised learning process. The Bb branch of the DON processes the operator input. This input is generally a function or a set of values ​​that represent a function.

[0216] Branch Bb learns a representation of the input function. To do this, it may take as input samples of this function, for example, values ​​of the function at different points, and produce a higher-dimensional representation that captures some characteristics of this function.

[0217] This branch Bb allows to understand the structure and properties of the input function, allowing the network to respond correctly to variations in this input data.

[0218] The Bt branch is designed to process the points {yk]k of the domain for which the output of the operator is to be evaluated. The Bt branch produces a representation of these points. This representation is then used to predict the output of the operator at these specific points.

[0219] The Bt branch allows the DON network to understand how the operator acts on different parts of its domain, which helps improve the predictions of the DON model outputs.

[0220] The outputs of branches Bb and Bt are combined with each other to produce the final output of the network. This combination can be done in different ways. In one example, the combination is achieved by a scalar product.

[0221] By separately processing the operator input via branch Bb and the output points via branch Bt, the DON network can efficiently learn the relationship between the operator input and output. This separation allows for greater flexibility and accuracy in learning complex operators.

[0222] According to an example implementation, the DON network comprises only one branch Bb. Such a network is called in English terminology “unstacked DeepONet”. It has the advantage of being less consuming in matrix calculations.

[0223] According to an exemplary implementation of a DON network, an architecture of the network is configured such that the outputs of branches Bb and Bt are combined via a linear combination, such as a dot product, to produce the final output of the DON network.

[0224] According to one embodiment, the DON network takes into account physical constraints. The network is called “physics-informed DeepONet” in English terminology. Such a network makes it possible to take into account in the configuration of the loss function physical constraints making it possible to penalize predicted values ​​outside a predefined range of values. Loss functions

[0225] According to an example, the loss function Lf(0) of the DON network is configured to minimize a first term noted Lopé(0) which corresponds to the loss function of the operator and a second term noted Lphy(0) which corresponds to the loss function of the physical constraints.

[0226] According to one embodiment, when training the MLAi model, the loss function Lf(0) is configured to optimize an error by taking into account a factor making it possible to learn the operator Lopé(0) optimizing the error of a function u(x) modeling the geometry of the vessels and one making it possible to learn physical constraints Lphy(0) optimizing the error of a system of equations defining limits and a compatible domain of the physics induced by the Navier Stokes equations.

[0227] The step of calculating and optimizing the error calculated by the loss function is represented in [Fig.6] during the training of the MLAb model

[0228] The loss function can be written: Lf(0) = Lopé(0) + Lphy(0)

[0229] With, according to an example, the following expression of the two operators:

[0230] Where {yk(i)}ki àQ denotes a set of randomly sampled points in the domainG(u(i)).

[0231] Where N is a linear or nonlinear differential operator which gives the differential equations the following form: N(u, G) = 0

[0232] The physical constraints taken into account in equation [3] by the operator Lphy(0) can take the form of the system of differential equations resulting from the incompressible Navier Stokes equations.

[0233] This system of equations takes the form of a numerical model of hemodynamic equations- namics called MODi. It can be expressed as follows: 1 dq 1 d [Math 4] (¾. OX (7^ Ot 1 dq 1 d (q2\ 1 To dp 4 q "■—— ~—I —“ I H- ■— ——■ “—--z otr di dx \ J / oXr p dx ô'Re P ~Pû =

[0234] According to another embodiment, another system of hemodynamic equations may be used to define the MODi model or other equations may be integrated into the MODi model of equations [4]. These hemodynamic equations may be modeled in 1D, 2D or 3D.

[0235] Other equations of state than that of pressure can also be used.

[0236] According to one embodiment, the empirical equation for calculating Young's modulus is used as described for CFD.

[0237] According to one example, the Navier Stokes equations are represented in a non-dimensional manner and are integrated over the surface of the cross-section of the vessel or portion of vessel considered.

[0238] The parameters and variables are defined as follows: q .4 o Ao [Math 5] Qmax ^max Pmax ^max A2 max j^ma* . i „ iy 7T

[0239] We consider x as a coordinate along the Ox axis of vessel straightening, t is the time parameter, p is the pressure, q is the flow rate, A is the section, ô is the boundary of the layer thickness and v is viscosity.

[0240] In these equations, a new variable Re, denoting the Reynolds number, is introduced. The values ​​of the variables in a 1D one-dimensional model are considered as their known maximum values.

[0241] Furthermore, the method of the invention allows to consider as another target variable. For the additional variables q, p, % additional constraints have been defined, namely: Cç, C^, C^,

[0242] Thus, if the following intervals are violated, the cost function will penalize learning:

[0243] Q= [0 ; 1]

[0244] q=[0;l]

[0245] = [7e-06, 1]

[0246] CX()= [7-06, 1]

[0247] According to different embodiments, methods of optimization and minimization of each equation [4] of the MODi model described can be implemented to solve the system according to a residue or an error to be minimized. Model training

[0248] The invention also relates to a method for training the MLAb model. An advantage of the training method of the invention is to consider different sets of test and validation data E2, E3 and E4 coming from different training configurations to train the MLAi model.

[0249] [Fig.6] represents the MLAi model during these different training phases noted Bb B2, B3 allowing to obtain three inputs of the network to train it. Three inputs are represented on [Fig.6] by the blocks Bb B2, B3 allowing to better understand these different training phases. The test and validation data of each of these branches E2, E3 and E4 are represented at the output of the 3 data normalization blocks noted NML.

[0250] An advantage of training using different configurations is to obtain better predictions in the exploitation phase of the MLAi model.

[0251] Indeed, the first input aims to train the MLAi model with data tested in vivo, that is to say with patients for whom pressure measurements are carried out from a catheter. The second input aims to train the MLAi model with a CFD solver allowing to solve a system of incompressible differential equations of Navier Stockes. The third branch aims to train the MLAi model with data measured on a test bench, the measurements are said to be in vitro.

[0252] Such 3-phase training makes it possible to obtain an exhaustive panel of test data making it possible to obtain data representative of the real case, taking into account the physics equations and finally making it possible to model a large number of different stenose geometries.

[0253] According to one embodiment, the method of the invention may comprise a training based solely on a single input {BJ, {B2} or {B3}, or on two inputs {Bi, B2], {Bi, B3], {B2, B3] out of three. For example, according to one embodiment, the method of the invention only includes the training data {ENSi ”, E3} and {ENSi”', E4}. In this case the model is trained solely with data from the CFD solver and in vitro data.

[0254] When the training method comprises the first input Bi, in vivo tests can be conducted in order to obtain the data E2. In another case, the data E2 exists and is stored in a memory or a database. In the latter case, the method of the invention receives the data from a memory to train the model with the test data E2 that have already been collected.

[0255] Such training comprising the data from several inputs Bb B2 and B3 as represented in [Fig.6] makes it possible to obtain better predictions of the input pressure pa of a first vessel 10 and better predictions of the pressure on the axis up to the outlet of the vessel including the outlet pressure pd of the first vessel 10. The FFR deduced by the network thus trained is then more reliable depending on the specific case encountered. Input B2: CFD solver training data

[0256] A second input denoted “cfd” in [Fig.6] makes it possible to train the MLAi machine learning model. According to one embodiment, a set of training data corresponding to the test and validation data E3 is obtained by solving a so-called “1D CFD” model.

[0257] The 1D CFD equation system is for example applied to data acquired from a vessel geometry obtained from an imaging system. [Fig.6] represents this example case in which the anatomical data of the vessel 10 from the first segmentation SEGi of the first input Bi are used to provide anatomical data to the 1D CFD solver of the input B2. Arrow 19 represents the acquisition of this data. Second and third Segmentations SEG2, SEG3 for the CFD solver

[0258] The method of the invention comprises a second segmentation SEG2 of the first vessel 10 into different segments or portions. This step is noted SEG2 in [Fig.6]. The second segmentation step SEG2 is used in particular during the training phase jointly with the modeling model M0D2 of the hemodynamic flow also called CFD.

[0259] A third segmentation SEG3 can also be used during the training phase with in vitro test data. This training phase corresponds to the third branch of [Fig.6] called “in vitro”.

[0260] The third segmentation relates to a pipeline modeled on a test bench comprising portions into which a flow is injected and ca parameters characterizing the flow are measured. These data can then be used to train the MLAb model. The third segmentation aims to characterize sections of pipes having topological properties representing the different singularities of a vessel.

[0261] For this purpose, the training method of the invention makes it possible to automatically generate sectional plans of the vessel in order to consider each segment as a portion of vessel whose blood flow properties can be calculated using the hemodynamic model M0D2. One advantage is to calculate test values ​​to train the machine learning model.

[0262] During the second segmentation SEG2 used to associate the Navier Stokes flow equations with characteristic portions requiring a given model, characteristic cutting planes can be defined. These cutting planes can be automatically generated using an image processing algorithm.

[0263] [Fig.4] also represents different cutting planes generated in particular during the second segmentation SEG2. These cutting planes are noted pci, pc2, pc3, pc4 pc5, pc6 on [Fig.4]. They are generated to delimit the different types of portions in the second segmentation.

[0264] [Fig.4] represents different portions including a type of non-stenosed portion 6 and a type of stenosed portion STi, ST2.

[0265] In the example of [Fig.4], the delimitation planes pci and pc2 delimit a first non-stenosed portion 6, the planes pc2 and pc3 delimit a first stenosed portion STi, the planes pc3 and pc4 delimit a second non-stenosed portion 6 and the section planes pc4 and pc5 delimit a second stenosed portion ST2 and finally the section planes pc3 and pc4 delimit a third non-stenosed portion 6.

[0266] The section planes are shown in [Fig.4] to illustrate that after the section plane Pc3 or PC5 delimiting the end of a stenosed portion, a pressure drop may be a consequence.

[0267] During training, the use of the hemodynamic model M0D2 in the cfd branch of [Fig.6] allows the calculation of characteristic values ​​of the blood flow. The boundary conditions between the different portions considered allow the use of the equations in a data processing loop to integrate the results along the entire length of the vessel.

[0268] According to one embodiment, when using the hemodynamic model M0D2, called CFD, each segment considered corresponds to a physical type of the part of the vessel considered, namely a non-stenosed portion, a stenosed portion, a curved portion, a portion comprising a bifurcation. According to this embodiment, this rule makes it possible to define that two neighboring segments are always of different type.

[0269] [Fig. 11] represents an example of second segmentation SEG2 used for generate training data from a MOD2 clean hemodynamic equation model. In this model, different equations can be applied to different types of portions having a clean hemodynamic equation model.

[0270] [Fig. 11] represents a case of modeling several vessels with different bifurcations ABH AB2 and AB3 representing areas of junction between vessels.

[0271] An inlet of the blood flow is represented by the element IBi and the different outlets of the blood flow are denoted OBi, OB2, OB3 and OB4.

[0272] A first type of segments sgb sg3, sg4, sg6, sg8, sg9, sg10, sgn, sg13, sg14, sg16, sg17, sgi9, sg2b corresponds to the portions of the vessel in which the flow can be modeled by equations of the CFD solver, called 1D Navier Stokes equations noted [1] and [2], making it possible to model the flow and to calculate the pressures within the vessel(s) by considering initial hypotheses on the flow of the flow.

[0273] According to one embodiment, the method of the invention is carried out for each branch from the entry point IBi to the different exit points OBi, OB2, OB3 and OB4. The method of the invention makes it possible to obtain the pressure P(x, t), the flow rate Q(x, t) and the section A(x, t), that is to say at any point along each vessel and at each instant of the cardiac cycle.

[0274] According to one embodiment, a mesh is defined to model and solve the system. The number of cells of the mesh along the axis of the vessel and the time step are two control parameters. Other control parameters can be defined.

[0275] A second type of segments sg5, sg7, sg[2j sg20 corresponds to the portions of vessel exhibiting stenosis, i.e. a local reduction in the diameter of the vessel greater than a threshold. The portions exhibiting stenosis require the use of a dedicated flow circulation model different from the model used for circulation in a non-stenosed portion. In this case, an equation

[21] described below can be used to model the blood flow and to calculate the inlet and outlet pressures of each stenosed portion by considering initial hypotheses on the flow of the flow.

[0276] A third type of segments sg2, sg[8 corresponds to the portions of vessel with a curvature greater than a threshold and which can affect the circulation of the flow with respect to a circulation in a non-curved portion. In this case, an additional equation can be used to model the blood flow by considering initial hypotheses on the flow of the flow.

[0277] A fourth type of sgi5 segments corresponds to the portions of vessel presenting an aneurysm, that is to say the portions presenting a local bulge of the diameter of the vessel greater than a threshold. A local bulge can be detected due to a local increase in the internal and / or external diameter of the vessel greater than a threshold. The threshold can be expressed as an absolute value or as a proportion of the average vessel diameter or the diameter in an adjacent portion. The threshold can also be characterized by the local variation in diameter. Portions with a local bulge can be better modeled by requiring the use of a dedicated flow circulation model that is different from the model used for circulation in a portion of the first type for example. In this case, a semi-empirical equation similar to the equation

[21] described below dedicated can be used to model the blood flow by considering initial assumptions

[0278] Thus, the second segmentation operation is carried out automatically by first labeling the different portions of the vessel according to specific geometric characteristics.

[0279] In order to delimit the cutting planes during this second segmentation SEG2, the training method of the invention makes it possible to detect variations in diameters or radii of the first vessel. Thus, after a reduction in the diameter greater than a predefined threshold, for example expressed as a percentage of the average radius, the maximum radius or the local average radius before the reduction, a cutting plane can be generated. And identically, after an increase in the diameter greater than a predefined threshold, for example expressed as a percentage of the average radius, the maximum radius or the local average radius after the increase, a cutting plane can be generated. Continuity conditions at the boundaries of segmented portions

[0280] The second segmentation SEG2 makes it possible to define a continuity condition between two successive segmented portions, in particular with regard to the values ​​estimated by the different models M0D2 applied according to the type of segments. In particular, the pressure or flow rate at the outlet of a first portion is equal to the pressure or flow rate at the inlet of a second portion directly following the first portion. And conversely, the pressure or flow rate at the inlet of a second portion is equal to the pressure or flow rate at the outlet of a first portion directly preceding the second portion. This is also true for other parameters characterizing the flow or the boundary conditions at the junctions between segments.

[0281] Thus, it is possible to train the MLAi model by the estimated values ​​of the second hemodynamic flow model M0D2 within the training method of the invention by a step-by-step approach.

[0282] For this purpose, a feedback loop can be used in order to integrate the values ​​calculated by the application of the second hemodynamic model M0D2 on a plurality of segments linked together with the continuity conditions.

[0283] As regards the stenosed portions, a mathematical method for managing the boundary conditions can be implemented. For example, a so-called “ghost cell” method called in English terminology “ghost cells" can be implemented. These ghost cells are added to the mesh cells.

[0284] According to one embodiment, the feedback loop makes it possible to test which type of segment is processed in the loop for a given position before repeating the calculations for an incremented position. If the position considered in the feedback loop is a stenotic position, the method of the invention makes it possible to implement a ghost cell.

[0285] The principle is to define a physical grid of space allowing calculations to be carried out in which each cell represents a volume of fluid. The ghost cells allow boundary conditions to be defined on the pressure, flow rate, etc. in the ghost cells according to the boundary conditions of the problem. For example, the fluid velocity can be set to 0 to simulate the presence of a vessel wall. The conditions can be of different natures such as Dirichet conditions for fixed values ​​of the conditions or Neumann conditions for gradient type values ​​or more complex conditions such as sliding or periodicity conditions. For example, the condition on the time variable t can be induced from the heart rate constraint. The integration of the Navier Stokes conservation equations is carried out on each cell and also on the ghost cells.

[0286] When integrating the equations on each branch from the entry point IBi to the different exit points, stenosed or not, the boundary conditions given by the resolution of the Windkessel equations

[17] at the exit, that is to say in the case of [Fig.11], at the points OBi, OB2, OB3 or OB4, make it possible to resolve the equations from near to near.

[0287] [Fig.6] also represents the example case in which the anatomical data of the vessel 10 are obtained from the geometric data of the in vitro measurements, i.e. the geometric data of the training inputs B3. Arrow 18 represents the acquisition of these data coming from the PROD2 block.

[0288] The different geometry segmentations created in vitro can be used as many different scenarios for M0D2 modeling called CFD. One advantage is to produce a lot of training data to cover many scenarios. For example, cases in which several stenosed portions follow one another in the same vessel.

[0289] Furthermore, these geometry data from the 3rd SEG3 segmentation allow the validation of CFD models. Thus, the choice of equations, in particular equation

[21] for the stenosed portions or equivalent semi-empirical equations, can be adjusted to model certain portions of the vessel. For example, the coefficients kv and kT of equation

[21] can be adjusted according to the

[0290]

[0291] different geometries of stenotic portions or other coefficients can be calculated and fitted for other semi-empirical equations. In another case, the data are obtained from vessel data already stored in a memory. The data source is denoted PRODi in [Fig.6]. The geometric data are denoted Ei”. In an example case, the geometric data come from the same images as the in-vivo data from the Bi input in [Fig.6]. An interest is to allow comparing the CFD predictions with the in-vivo measured data. The 1D CFD model is obtained through an application of the Navier- equations Stokes for each segmented portion or group of portions of the first vessel 10. ITS , [Math 6] = 0 a ■ ' [Math 7] A op _ 4 g P gx ôRe ^A

[0292] Or: q=q / q , [Math 8] A = AIA^X -4 , [Math 9] , [Math 10] v; 7“

[0293]

[0294]

[0295] We consider x as a coordinate along the Ox axis of vessel straightening, t is the time parameter, p is the pressure, q is the flow rate, A is the section, ô is the thickness of the boundary of the layer wall and v is viscosity. Equations (1) and (2) can be derived with an assumption of uniform pressure within a section of the vessel. The speed profile is denoted here by u and can be expressed as follows: II \ü(R—r) / b, R—b <r^R [Math 11]

[0296] According to one embodiment, additional terms, such as gravity, may be included in the equations or even different speed profiles.

[0297] According to one embodiment, an equation of state that associates the pressure and the surface area of ​​the vessel section can also be added to the system of equations: / \,[Mathl2]

[0298] Where:------ , [Math 13] Eh, [Math 14] Eh =-----; ? v

[0299] With the following definitions of the constants or parameters taken into consideration: , [Math 15]

[0300] po and r0 are the pressure and radius of the vessel at equilibrium

[0301] E is Young's modulus.

[0302] h is the thickness of the vessel.

[0303] According to one embodiment, the experimental data give the following relationship making it possible to link these latter parameters: Eh, tr, .[Math 16] ——k> c " k r 1 ' o

[0304] Where

[0305] kj = 2.107 g / (s2«cm)

[0306] k2 = 22.53 cm-1

[0307] k3 = 8.65* 105 g / (s2.cm)

[0308] Relation (4) may, according to certain embodiments, integrate elasticity effects such as viscoelasticity without affecting the structure of the CFD solver.

[0309] According to one embodiment, the thickness of the wall of a vessel is a constant of the system. The method of the invention takes into account a default value. According to one embodiment, the thickness of the vessel can be modified according to parameters such as parameters of the individual profile: such as their age or gender and parameters extracted from the imaging. According to one embodiment, the thickness of the vessel considered is taken into account in the vessel elasticity model.

[0310] The boundary conditions allow equations [6] to

[10] to be solved. The boundary conditions are given at the entrance and exit of the vessel considered.

[0311] Boundary conditions can be obtained directly or deduced indirectly from experimental measurements.

[0312] According to one embodiment, among the values ​​which are used for the boundary conditions, we find the resistance Riou, the characteristic impedance Zc, the resistance R 2 and the compliance C.

[0313] The outlet conditions can be obtained from the Windkessel equation. The latter is written as a function of the pressure p and flow q parameters: A. Rjl dq pp, A [Math 17] q+C —--— -p- — —---— + C —---—pr RY + R2 dt R^ + R2 R}+ R^ dt

[0314] Where: " , [Math 18]

[0315] This equation is true for: - the impedance Zc, noted Ri in equation

[17] ; - the following equality: R = Ri+ R2.

[0316] Different ways can be used to determine the coefficients of resistance R or R2 and compliance C and impedance Ri or Zc,

[0317] According to one embodiment, values ​​of constants Ri or Zc, R2, and C can be estimated from the in-vitro data using the pressure wave propagation speed, noted PWV and designating in English terminology “pressure wave velocity”. It is calculated using two distant pressure sensors considering a known distance.

[0318] The impedance Ri and the compliance C can be obtained for example from the following equations: / C ■ - p * FWVM [Math 19] . 1, [Math 20] GP < [PW)2

[0319] According to another example, values ​​of constants Ri or Zc, R2 and C can be considered according to the values ​​published in the literature.

[0320] However, these methods do not allow values ​​to be adjusted and adapted to each individual.

[0321] Thus, training the machine learning model makes it possible to learn the learning function from the in-vivo measured data and the CFD model.

[0322] The invention makes it possible in a second step, when the machine learning model has been trained, to deduce these values ​​from the application of the MLAi machine learning model with operating data coming from the ENSp data set.

[0323] Equations [6] to

[15] with the boundary conditions given by the Windkessel model

[17] make it possible to solve the 1D CFD solver for vessel branches not having stenosis or more generally not being obstructed.

[0324] For portions having a stenosis, a bifurcation, or an aneurysm, a semi-empirical equation can be used and solved.

[0325] For example, in the case of a stenosis, according to one embodiment, a semi-empirical model expressing a pressure delta, available in the literature, can be used: / ; U, [Math 21] ^PA,' KV^AS K, A. ——v ^-1 P 4S “ e A \ 1 y

[0326] where Kv and Kt are the viscous and turbulent resistance coefficients, and the indices s0 and Si refer to the values ​​immediately before the stenosis and inside the stenosis respectively.

[0327] Such a model is called the first model of a pressure delta.

[0328] In this example, we consider that the cross-section is constant over its entire length of the stenosis. We specify here that the notations are similar to those of the output of the MLAi model noted Si, however, they do not represent the same variables or parameters.

[0329] This expression is linked to a geometry as a whole and cannot be resolved for a point x of the Ox axis and a given instant t.

[0330] The precise expressions of the coefficients Kv and Kt can be obtained experimentally or the data can be obtained from the scientific literature.

[0331] Equation

[21] can be modified for each profile of [Fig. 10] according to experimental tests. For this purpose the test bench of [Fig.8] can be used to reproduce a flow environment close to a vessel under given flow conditions.

[0332] For this, each portion of vessel can be characterized by its type: simple portion, curved portion, portion comprising a narrowing, or even a portion comprising a dilation.

[0333] In each of these portions, a pressure delta can be measured by an experimental method using sensors.

[0334] The measurements made can be used to define the viscous resistance coefficients kv and the turbulent resistance coefficients kT for each identified portion. One advantage is to use a test bench 20 making it possible to estimate the flow characteristics of a fluid to estimate the coefficients kv and kT in a second step.

[0335] A method for estimating these coefficients may be based on the implementation of a machine learning model making it possible to learn the coefficients from a plurality of measurements of which the values ​​characterizing the flow of the fluid due to the test bench are known.

[0336] Equations [6] to

[15] can be solved numerically for example from the MacCormack method considering a given order of the system and the boundary conditions. The 1D CFD model can be applied to cases of different complexity, from a single unobstructed vessel to a network of branched vessels with multiple singularities such as stenosis, bifurcation, aneurysm, etc. In order to translate the geometry obtained by the sensors into a form suitable for numerical simulation, the pre-processing software identifies and divides the complete geometry into a set of "segments" and creates a topological diagram describing their interconnection as shown in [Fig. 11].

[0337] Each segment represents a section of the vessel corresponding to one of the predefined types, for example an unobstructed straight vessel, an unobstructed curved vessel, a vessel with stenosis, a bifurcation, etc. Each segment is also characterized by a set of variables such as its length, its diameter, its type, the neighboring segments with which it interacts, etc.

[0338] If the system of the modeled vessel(s) includes one or more bifurcation points, the entire calculation area is divided into "branches", each branch being composed of a continuous set of segments between the segments containing the entrance or bifurcation and the exit boundaries. An example of a bifurcation is shown in [Fig.11] at the junction points ABb AB2, AB3.

[0339] The values ​​of the characteristic parameters of the stenotic portions are solved from equation

[21] .

[0340] Suitable equations such as equation

[21] are used in "special" segments e.g. a segment with stenosis, etc. The 1D CFD model is designed to be easily adaptable to the introduction of various types of "special" segments, requiring specialized treatment, as well as to modifications of the equations governing the baseline, which is accomplished by a set of switches activating different formulations of equations [6] to

[15] e.g., various treatments of elasticity

[12] and

[15] , velocity profile

[11] or boundary conditions

[17] .

[0341] The resolution of the system makes it possible to provide the data allowing the MLAi model to be tested during training and to validate the latter to obtain a prediction with a sufficient confidence score.

[0342] A data normalization step can be carried out, noted NML in [Fig.6]. This data normalization phase has two objectives: on the one hand, to normalize the data from different training sources and on the other hand to train the model with data having the same format, the same ranges of values ​​as the data processed during the exploitation of the trained MLAi model.

[0343] The normalization step in the training from the simulations of the second model M0D2, called CFD modeling, is also used to improve stability by ensuring that all primary variables have comparable magnitudes. Entry B3: Training with in vitro measurements

[0344] A third input B3 noted "In vitro" in [Fig.6] makes it possible to train the MLAi machine learning model. According to this method, a test bench 20 is defined so as to control a flow geometry and measurements at different characteristic points. Such a bench has the advantage of making it possible to carry out thousands of experiments reflecting different configurations without requiring testing on patients. In order to train the model, measurements can be carried out in different ways. One method aims to model portions of pipes and to measure the fluidic and mechanical properties of the flow within these portions, for example by measuring the pressure from a pressure sensor, the flow rate from a sensor or Doppler-type ultrasound, the viscosity from a viscometer, the elasticity for example from a tensile test.

[0345] Many parameters can be adjusted, such as resistance R, impedance Zc, compliance C and for example the following parameters: • The radius of the 3D printed artery, expressed in cm • the length of the segment, expressed in cm • the maximum speed noted Up, expressed in cm / s • the pulsation noted f or fc expressed in Hz / 60 • the flow rate Q, expressed in ml / min • viscosity, expressed in Pa*s • the density expressed in kg / m3 • the Reynolds number noted Re • the equilibrium pressure noted Po and expressed in mmHg • elasticity noted E, and expressed in Mpa or compliance C which is linked to the elasticity value • the gravity vector

[0346] The parameters can be adjusted for example by the choice of the properties of the materials used, the choice of the thickness of the parts used, the method of manufacturing the part such as 3D printing or molding the part, and their configuration or arrangement between them or within the bench.

[0347] An example of a test bench 20 modeling the flow of fluid within different portions is shown in [Fig.8]. Such a representation is illustrated as an example, other examples of test benches can be produced within the framework of the present invention. An advantage of this test bench is that it allows any type of segmentation to be represented. This test bench 20 can correspond to a third segmentation SEG3 which can, for example, imitate or not concrete cases of vessels in vivo.

[0348] The test bench 20 may comprise an inlet 26, a main flow channel 25, a test section 23, a return flow channel 27, a pump 21, pressure sensors 24.

[0349] During such tests, the pressure sensors 24 make it possible to record inlet and outlet pressures for portions to be tested having different geometries.

[0350] Portion 30 represents a curved portion that can be tested under the same conditions as a straight portion. Portion 32 allows a bifurcation to be modeled. Portion 33 allows a narrowing of the canal to be tested and aims to model a stenosis.

[0351] [Fig.9] represents different portions of bifurcation 32 with parameters characterizing the angle alpha between the bifurcated portions which and characterizing the diameters di and d2 of said bifurcated portions.

[0352] [Fig. 10] shows different geometries 33 modeling various ST stenoses by different channel narrowings and different topologies. These geometries can be used to generate many test bench configurations 20 and thus adjust the coefficients kv and kT of equation

[21] according to the topology of the singularities describing a stenosis likely to be present in a vessel.

[0353] Narrowing profiles are noted such that profile P defines a narrowing along straight lines. An S20 profile defines a narrowing along curved lines. An S1 profile defines a narrowing along curved lines with an asymmetry of variation of the narrowing between the downstream portion of the stenosis and the upstream portion of the stenosis. The S30 profile has an inverse asymmetry with respect to the S10 profile. The PU profile has a narrowing with straight lines comprising an asymmetry within the section. The SU profile has a variation of diameter within the asymmetric stenosed portion between the upper part and the lower part. of the vessel. The PU2 profile also exhibits asymmetry and an induced flow orientation along an axis that is not collinear with that of the vessel. It is possible to use two profiles from [Fig. 10] to simulate a case in which two or more stenoses are present, as in the case of [Fig. 4].

[0354] The geometric data thus modeled can be used to produce numerous scenarios. The source of this data is noted PROD2 in [Fig.6]. The PROD2 source corresponds to the production of the input anatomical descriptors used to define the ENS / ” input data of the MLAb model.

[0355] As in the context of CFD, the PROD2 component makes it possible to produce the geometric data and the data of all the in-vitro measurements Q, P, A from the sensors placed on the test bench 20.

[0356] According to one embodiment, when training the MLAB machine learning model, pressure and flow rate measurements at different points of the test channel can be measured using appropriate sensors, in particular pressure sensors. These values ​​are used to train the model.

[0357] During training, according to one embodiment, it is possible to measure the values ​​of the following parameters at several points of the channel: • the flow rate Q(x,t) for example at any point from a Doppler type ultrasound • the pressure P(t) at different points, for example 5 to 10 points, and • A(t) at different points, for example 5 to 10 points.

[0358] In addition, the equilibrium pressure Po, the viscosity, as well as the resistance R, the compliance C and the impedance Zc at the output of the branch considered, can also be measured.

[0359] It is therefore possible to test the values ​​predicted by the MLAi learning model using the measured values.

[0360] The measured data define the E4 data represented in [Fig.6]. The E4 data allows the model to be tested during supervised training and the MLAi machine learning model to be validated to obtain a confidence score of the desired predictions. In this regard, the E4 test data can be fragmented into different sets so as to define an optimized training phase.

[0361] The geometric data and the measured data are denoted ENSf” and E4 in [Fig.6]. The geometric data are defined so as to be normalized identically to the training data Ef or Ei” or the operating data set Ei of the MLAi model.

[0362] This normalization step is noted NML. This normalization step makes it possible in particular to process multi-fidelity training data coming from different systems.

[0363] One approach to combining various data sources is to consider them in the context of so-called "multi-fidelity" methods. Multi-fidelity methods, denoted MF, represent a significant advance in the field of computer science, particularly for complex models that require significant computing resources. These methods combine high-fidelity data that are accurate but expensive to obtain, for example, by means of in-vitro, in-vivo tests, and low-fidelity data that are less accurate but less expensive, such as the CFD solver, to improve the accuracy of the prediction.

[0364] The multi-fidelity method approach is particularly advantageous in optimization and uncertainty quantification applications because it reduces the need for high-fidelity model evaluations, such as in vitro measurements. Multi-fidelity models can use Gaussian process regression or nonlinear autoregressive network architectures to correlate the different fidelity levels. Entry B1: Training with in vivo measurements

[0365] A first input Bi and noted "In-vivo" in [Fig.6] makes it possible to train the MLAi machine learning model from data coming from patients. The notation "In vivo" does not necessarily refer to manipulations carried out on a living being, but refers to the fact that the data come from living beings, more particularly from humans. The ENS2' patient data used are recorded in a memory before their use.

[0366] The method comprises a phase of training the MLAi machine learning model using in-vivo measurements. The measurements can be carried out from a catheter introduced into an artery or vessel of a patient. The catheter advantageously has at least one pressure sensor. The pressure readings are taken at different points identified on the acquired and straightened image of the vessel. During these measurements, the measurements are preferably carried out at different times in the cardiac cycle and with different heart rates. In addition, the in-vivo flow rate can be measured by different methods, including Doppler-type ultrasound, thermodilution, etc.

[0367] According to one embodiment, demographic data, patient history data, and functional data such as systolic / diastolic pressure, cardiac MRI measurements, and cardiac ultrasound may be measured. Other data may also be collected and used in various embodiments.

[0368] Laboratory measurements, including hematocrit and protein, can be used, for example, to estimate viscosity.

[0369] Alternatively, the training method of the invention does not comprise the measurement step, but only a step of reading data already acquired and recorded in a memory.

[0370] The collected data set can then be used to learn an MLAb machine learning model. In this scenario, the geometry of the vessel is acquired by an imaging system. The vessel of interest is segmented and the portions without stenosis and with stenoses are identified as described previously in the FFR estimation method.

[0371] The training data, for the in vivo case, in this case comprise the test data E2 represented in [Fig.6]. According to one embodiment, the training data comprise on the one hand the ENSf data extracted from the anatomical descriptors and the ENS2' data called patient data as well as the measured data E2 making it possible to validate the predictions made by the MLAi model.

[0372] The training data can be split into different groups so as to test to define supervised training and to validate the model to obtain a sufficient confidence score.

[0373] List of equations [Math n]

[0374] [1]: Function model of a DeepONet type machine learning model or “Physically informed DeepONet”;

[0375] [2]: equation of a loss function specific to the modeling of the reduction of loss related to the mathematical operator;

[0376] [3]: equation of a loss function specific to the modeling of the reduction of loss related to the mathematical operator;

[0377] [4] ; Navier Stokes equations defining the MODi model to constrain the loss function of the MLAi learning model;

[0378] [5]; standardized expressions of the different variables / parameters of the equations [4];

[0379] [6]: Navier Stokes mass conservation equation defining the second M0D2 model also called CFD model or CFD solver;

[0380] [7]: Navier Stokes equation of conservation of motion defining the second model M0D2 also called CFD model or CFD solver;

[0381] [8]: equation allowing the estimated values ​​to be normalized, in particular of the section, of the position and thickness of the wall;

[0382] [9]: equation allowing to normalize the estimated values ​​in particular of time and of pressure and in particular in equations

[61] and

[72] ;

[0383]

[10] : expression of the Reynods number;

[0384]

[11] : equation describing the speed profile;

[0385]

[12] : pressure equation of state;

[0386]

[13] : normalized expression of the radius of the vessel at equilibrium;

[0387]

[14] normalized expression of Young's modulus notably used in the equation [7]

[0388]

[15] : Equation of the section of the vessel at equilibrium;

[0389]

[16] : Empirical equation for calculating Young's modulus;

[0390]

[17] : Windkessel equation;

[0391]

[18] : normalized expression of the resistance and impedance coefficients of equation

[17] ;

[0392]

[19] : expression of the impedance from a measurement of the propagation speed of a pressure wave;

[0393]

[20] : expression of compliance from a measurement of propagation speed of a pressure wave;

[0394]

[21] : semi-empirical equation modeling the flow within a stenosed portion.

Claims

Claims

1. Method for estimating the coronary reserve flow fraction (FFR) of a vessel comprising: • Acquisition (ACQi) of at least a first image (IMi) from an imaging system; • Extraction (EXTi) of a first set of data (ENSi) defining anatomical descriptors of a first vessel (10) from said first image (IMi); • Acquisition (ACQ2) of a second set of data (ENS2), called patient data, comprising at least the heart rate (fc) and the myocardial mass (Mc); • Generation of an input (Ei) comprising the first set (ENSi) of data, the second set of data (ENS2);• Generation (GENi) of an output (Si) defining a prediction of a quantity of coronary flow reserve fraction (FFR) by means of the execution of a first machine learning model (MLAi) to produce an output (Si), said first machine learning model (MLAi) implementing a parameterizable loss function (Lf) including at least a first factor (Lphy) modeling at least one parameterized physical constraint optimized during the training of said model (MLAi), said parameterized physical constraint resulting in particular from a first numerical model of hemodynamic equations (MODi).;

2. Method according to claim 1 characterized in that the extraction of the first set of data (ENSi) is obtained thanks to a first segmentation (SEG1) of a representation of a set of vessels acquired by the imaging system, said extraction resulting from a selection of at least one first vessel (10) displayed on a display, the selection of a point of the vessel.

3. Method according to any one of claims 1 to 2 characterized in that the anatomical descriptors are extracted from a representation (2) of the first vessel (10), at least one first descriptor comprising data characteristic of the radius or diameter of the section in each position of the first vessel (10) and at least one second descriptor comprising the positioning within the length of the vessel (10) of at least one narrowing of the diameter defining the presence of at least one stenosis (ST, STB ST2).

4. Method according to claim 3 characterized in that the second descriptor comprises data characteristic of the inlet section of at least one portion defining the narrowing of the first vessel (10) and data characteristic of the outlet section of at least one portion defining the narrowing of said first vessel (10).

5. Method according to any one of claims 3 to 4 characterized in that the extracted anatomical descriptors also comprise: • A third descriptor corresponding to the local curvature of the vessel and / or; • A fourth descriptor corresponding to the length of a stenosis (ST, STB ST2) and / or; • A fifth descriptor corresponding to a local dilation of the vessel (aneurysm).

6. Method according to claim 1 characterized in that it comprises the estimation of the flow rate of the incoming blood flow (Qrest) at rest from at least the heart rate (fc), the systolic pressure (Psyst) and the myocardial mass (Mc), the second set of data (ENS2) comprising the value of said flow rate of the incoming blood flow (Qrest).

7. Method according to claim 1 characterized in that it comprises the estimation of the flow rate of the incoming hyperemic flow at rest from at least the heart rate (fc), the systolic pressure (Psyst) and the myocardial mass (Mc), the second set of data (ENS2) comprising the value of said flow rate of the incoming hyperemic flow.

8. Method according to claim 1 characterized in that the second set (ENS2) of patient data comprises in particular: • An age of the individual; • A gender of the individual; • A diabetes indicator of the individual; • A hypertension indicator of the individual.

9. Method according to any one of claims 1 to 8 characterized in that the first machine learning model (MLAi) is a network DeepONet whose loss function (Lf) integrates a second factor (Lopé) defining a loss function of a differential mathematical operator.

10. Method according to any one of claims 1 to 9 characterized in that the first factor (Lphy) is modeled during the training of the machine learning model (MLAi) by a parametric function whose parameters are dependent on the solutions of the equations of the numerical model of hemodynamic equations (MODO characterizing the hemodynamic flow in the first vessel (10), said parametric function being implemented by a continuous non-linear operator, the resolution of said parametric function making it possible to generate value limits outside of which the cost function (Lphy) is penalized.

11. Method according to claim 10 characterized in that the equations characterizing the hemodynamic flow in the first vessel (10) to optimize the cost function (Lphy) and modeled by the first hemodynamic numerical model (MODO which comprises a system of equations comprising: • A mass conservation model; • A momentum conservation model; • A pressure equation of state.

12. Method according to one of the preceding claims, characterized in that it comprises a training step (B3) carried out from a third set of training data (ENS / ”, E4) characterizing portions of pipes each modeling an irregular geometry characteristic of at least one predefined section profile, the training of the machine learning model (MLAi) being supervised so that the values ​​characterizing the flow of a fluid in each portion are measured on a test bench (20) comprising at least one portion of test pipe and sensors making it possible to measure test data (E4) at different points of said test bench (20) comprising in particular the flow rate, the pressure, the viscosity, the resistance of the fluid, the Reynolds number and the density of the fluid.

13. Method according to claim 12 characterized in that it comprises a characterization of the different portions of the test bench (20), each portion being characterized by an artery radius to be modeled, an artery length to be modeled, an elasticity or compliance (C) and a portion type.

14. Method according to claim 13 characterized in that it comprises a pump, a clock and a means of recording a pumping frequency so as to inject a fluid into the test bench (20) reproducing a periodic activity relating to the cardiac cycle characterizing the different portions of the test bench (20).

15. Method according to any one of claims 13 to 14 characterized in that the third data set (ENS / ”) also comprises a measurement and a calculation for at least one point of each predefined portion of pipe: • of at least one output resistance (R, R2) modeling the force which opposes the flow of blood in the portion of the first vessel (10); • of at least one impedance (Zc, Ri); • of at least one viscosity value of the fluid; • of at least one value of the pressure (Po) at equilibrium.

16. Method according to any one of claims 1 to 15 characterized in that it comprises a training step (B2) carried out from a second set of training data (ENSi”, E3) characterizing the geometry (ENSi”) of portions of vessels obtained from an imaging system, the training of the machine learning model (MLAi) being supervised so that the values ​​characterizing the flow of a fluid in the first vessel (10) are estimated by a second model of hemodynamic equations (M0D2) called numerical solver (CFDi), to define test and validation data (E3) of the machine learning model (MLAi).

17. Method according to claim 16 characterized in that a second segmentation (SEG2) of the first vessel (10) automatically generates a plurality of types of segments (6, STi, ST2) including: • a first type of segment (6) defining substantially regular portions corresponding to portions of vessels having a section gradually decreasing from a proximal end towards a distal end; • a second type of segment (ST, STi, ST2, sg5, sg7, sg12, sg20) defining at least one irregular portion, said at least one irregular portion corresponding to a portion comprising at least one narrowing of the diameter greater than a predefined threshold, each of the sets of segments having a system of equations modeling the hemodynamic flow in said portion.

18. Method according to any one of claims 16 to 17 characterized in that the second segmentation (SEG2) of the first vessel (10) automatically generates a plurality of segment types (6, STb ST2) including: • a third segment type (sgi8) characterized by the presence of a local curvature of the vessel greater than a predefined threshold and / or; • A fourth segment type (sgi5) characterized by a local dilation of the vessel (aneurysm).

19. Method according to any one of claims 16 to 17 characterized in that the numerical solver (CFDi) comprises a system of equations characterizing the physics of the flow of a hemodynamic flow from the incompressible Navier Stokes equations applied to at least one portion of a vessel of a single dimension.

20. Method according to claim 19 characterized in that the system of equations comprises a second hemodynamic numerical model (M0D2) comprising for each portion of vessel at least one model among which: • A mass conservation model and / or; • A momentum conservation model and / or; • A pressure equation of state and / or; • A first model of a pressure delta and / or; • A second model of a pressure delta established from in-vitro measurements.

21. Method according to any one of claims 16 to 20 characterized in that it comprises a calculation of the blood flow characteristics in each portion of the first vessel (10) at each point of the axis of the vessel from the second hemodynamic model (M0D2) applied locally to each of the portions.

22. Method according to one of claims 16 to 21 characterized in that the second hemodynamic digital model (M0D2) makes it possible to estimate for each portion of vessel of the second type (ST, STb ST2) a pressure delta from a pressure delta model comprising a viscous resistance coefficient (kv) and a turbulent resistance coefficient (kT).

23. Method according to one of claims 16 to 21 characterized in that the second hemodynamic digital model (M0D2) makes it possible to estimate for each portion of vessel of the second type (ST, STb ST2), of the third type (sgi8), and / or of the fourth type (sgi5) a pressure delta from a pressure delta model comprising a viscous resistance coefficient (kv) and a turbulent resistance coefficient (kT), said coefficients being estimated from tests carried out on an in vitro test bench (20) of one of claims 12 to 15, said measurements carried out on the test bench (20) making it possible to estimate flow characteristics of a fluid.

24. Method according to any one of claims 16 to 21 characterized in that the first machine learning model (MLAi) is trained by considering the values ​​estimated by the second model (MOD 2) integrated over the entire first vessel (10).

25. Method according to one of the preceding claims, characterized in that a first set of training data (ENSf, ENS2', E2) comprises geometry data (ENS / ) extracted from a patient vessel imaging system, patient data (ENS2') comprising at least the heart rate (fc), the systolic pressure (Psyst) and the myocardial mass (Mc) and test and validation data (E2) from pressure measurements at different points of the portion of vessel considered.

26. A method of training a machine learning algorithm to produce a trained network (MLAi) for calculating the pressure of a fluid at a plurality of positions within a first vessel (10) as a function of time within the cardiac cycle, said training method comprising: Acquisition of a first set of training data (ENS / , E2) from: • Acquisition (ACQi) of a first image (IMJ of an imaging system; • Extraction (EXTi) of a first data set (ENS / ) defining anatomical descriptors of a first vessel (10) of said first image (IMi); • Acquisition of a third set of data (ENS / ), called patient data, including at least the heart rate (HR) and the myocardial mass (Mc); • Reading data (E2) characterizing pressure measurement points of a first vessel (10) defining test and validation data of a machine learning model (MLAi); Execution of the machine learning model (MLAi) and learning by implementing a cost function minimizing the error between data produced (S2) by the model (MLAi) and the test and validation data (E2); Acquisition of a second set of training data (ENS / ', E3) from: • Acquisition (ACQi) of a first image (IMJ of an imaging system; • Extraction (EXTi) of a first data set (ENSi”) defining anatomical descriptors of a first vessel (10) of said first image (IMJ; • Resolution of a solver (CFDi) modeling a model (M0D2) of hemodynamic equations from the incompressible Navier Stokes equations in one dimension, the data estimated (E3) by the solver (CFDi) defining test and validation data for a machine learning model (MLAi); Machine learning model execution (MLAi) and learning by implementing a mi cost function minimizing the error between data produced (S3) by the model (MLAi) and the test and validation data (E3); Acquisition of a third set of training data (ENSi”, E4) from: • Modeling of a set of geometries defining pipes suitable for conveying a fluid whose viscosity is substantially that of blood and suitable for being arranged within a test bench (20); • Performing a set of fluid flow tests with a variety of different geometries within the test bench (20); • Data measurement (E4) characterizing pressure measurement points of a first portion of channel defining test and validation data for a machine learning model (MLAi); Execution of the machine learning model (MLAi) and learning by implementing a cost function minimizing the error between data produced (S4) by the model (MLAi) and the test and validation data (E4).

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