Computer-implemented method for estimating fractional flow reserve and system

Abstract

The invention relates to a method for estimating the fractional flow reserve (FFR) of a vessel, including: - acquiring (ACQ1) a first image from an imaging system; - extracting (EXT1) a first data set (ENS1) defining anatomical descriptors of a first vessel; - acquiring (ACQ2) a second data set (ENS2) including at least the heart rate, the systolic pressure and the myocardial mass; and - generating (GEN1) an output (S1) defining a prediction of a fractional flow reserve (FFR) quantity by executing a first machine learning model (MLA1) to produce an output (S1), the first machine learning model (MLA1) implementing a parameterisable loss function including at least a first factor modelling at least one optimised parameterised physical constraint when training the model (MLA1), the parameterised physical constraint resulting in particular from a digital model of hemodynamic equations (MOD1).

Description

[0001] Description

[0002] Title: COMPUTER-IMPLEMENTED METHOD FOR ESTIMATING THE FRACTION OF CORONARY RESERVE FLOW, SYSTEM

[0003] Field of invention

[0004] 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.

[0005] State of the art

[0006] Currently, the characterization of coronary flow in a patient, particularly to consider whether or not to place a stent in the case of the presence of stenoses impacting coronary reserve, involves numerous steps to be implemented and generally requires an invasive intervention in the patient.

[0007] One of the most important variables in the evaluation and characterization of coronary flow is the coronary flow reserve, called FFR, which means "Fractional Flow Reserve" in the English literature. Generally, the measurement of FFR with the required precision is carried out using invasive coronary angiography by inserting a catheter with a pressure sensor. Indeed, FFR can be expressed as the ratio between two pressures measured upstream and downstream of a vessel, considering an upstream pressure measured at the ostium in order to characterize the coronary flow of the vessel. Certain FFR values ​​may lead to patient monitoring, one or more in-depth examinations, or even an intervention for the placement of a stent.

[0008] 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.

[0009] 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 of patients with 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 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.

[0010] Other solutions such as the one described in patent document WO2023 / 172970 mention exemplary implementations based on machine learning algorithms trained on patient data. This solution aims to estimate the FFR. A disadvantage of this method is that it is trained only on patient data. It is necessary to carry out measurements on many patients in order to cover the entire training domain.

[0011] However, a major constraint is that data collection during training requires measuring variables invasively and at different points in each vessel. Therefore, there is currently no training of a machine learning model based on in vivo training data that would allow the construction of a reliable model.

[0012] There is therefore a challenge in proposing a reliable, robust and non-invasive alternative to existing solutions.

[0013] Summary of the invention

[0014] According to one aspect, the invention relates to a method for estimating the coronary reserve flow fraction of a vessel comprising: ■ Acquiring at least one first image from an imaging system;

[0015] ■ Extraction of a first data set defining anatomical descriptors of a first vessel of said first image;

[0016] ■ Acquisition of a second set of data, called patient data, including at least heart rate and myocardial mass;

[0017] ■ Generating an input comprising the first data set and data generated from the second data set;

[0018] ■ Generating an output defining a prediction of a coronary reserve flow fraction quantity by means of executing a first machine learning model and inputting 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.

[0019] 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 learning of the machine learning model more efficient, in particular by using heterogeneous training data, i.e., data from different sources.

[0020] According to one embodiment, the extraction of the first data set 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. An advantage is to make the most of the images acquired by an imaging system, in particular to extract anatomical data.

[0021] 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.

[0022] 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.

[0023] According to one embodiment, the extracted anatomical descriptors also include:

[0024] ■ A third descriptor corresponding to the local curvature of the vessel and / or;

[0025] ■ A fourth descriptor corresponding to the length of a stenosis and / or;

[0026] ■ A fifth descriptor corresponding to a local dilation of the vessel (aneurysm).

[0027] One advantage is that it allows 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.

[0028] According to one embodiment, the method comprises estimating the rate of incoming blood 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 rate of incoming blood flow.

[0029] One advantage is having measurable input data for each patient, which allows for a better estimation of the outlet pressure at each point of the first vessel.

[0030] 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.

[0031] 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.

[0032] According to one embodiment, the second set of patient data notably comprises:

[0033] ■ An age of the individual and / or;

[0034] ■ A gender of the individual and / or;

[0035] ■ An indicator of the individual's diabetes and / or;

[0036] ■ An indicator of the individual's hypertension and / or;

[0037] ■ A weight of the individual and / or;

[0038] ■ A size of the individual and / or;

[0039] ■ Background data such as the existence and number of previous percutaneous coronary intervention(s), the existence and number of myocardial infarctions, quantification of tobacco consumption.

[0040] One advantage is having personalized input data, especially from data that can be collected easily and allows for improved prediction of output pressure based on the patient profile.

[0041] According to one embodiment, the first machine learning model is a DeepONet network whose loss function further incorporates a mathematical operator.

[0042] 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.

[0043] According to one embodiment, the first machine learning model is a multi-fidelity model comprising a first high-fidelity block and a second low-fidelity block, each block comprising a first sub-network defining a main branch considering as input the parameters of an input function sampled at specific points and a second sub-network defining a Trunk branch considering as input the coordinates of the specific points where an operator is to be evaluated. According to one embodiment, the patient data of the first set defines the inputs in the main branch of the high-fidelity and low-fidelity blocks, and the patient data of the second set defines the inputs in the Trunk branch of the high-fidelity and low-fidelity blocks.

[0044] 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 limits outside of which the cost function is penalized.

[0045] 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 comprises a system of equations comprising:

[0046] ■ A model of conservation of mass;

[0047] ■ A model of conservation of momentum;

[0048] ■ An equation of state for pressure.

[0049] An advantage is to take into account several constraints characterized by different physics equations and allowing to limit the training domain.

[0050] 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. An advantage of making it possible to generate numerous training data taking into account numerous anatomical geometries without requiring testing a large variety of vessel geometries of different patients.

[0051] According to one embodiment, the method comprises a characterization of the different portions of the test bench, each portion being characterized by an artery radius to be modeled, an artery length to be modeled, an elasticity or a compliance and a type of portion.

[0052] According to one embodiment, the method comprises an injection of a fluid into the test bench reproducing a periodic activity relating to the cardiac cycle characterization of the different portions of the test bench from a pump, a clock and a means of recording a pumping frequency.

[0053] An advantage is that it allows for the control of a wide variety of in vitro model parameters and the simulation of different virtual patients representing a diversity of patients.

[0054] 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:

[0055] ■ at least one output resistance modeling the force that opposes the flow of blood in the portion of the first vessel;

[0056] ■ of at least one impedance;

[0057] ■ at least one fluid viscosity value;

[0058] ■ of at least one value of the basic pressure at equilibrium.

[0059] One advantage is that it allows the calibration of a test bench with characteristics similar to real vessel anatomical features.

[0060] 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. An advantage is to have a large possibility of training from medical data such as real patient images whose values ​​and characteristics of the flow can be estimated to train the machine learning model of the invention.

[0061] According to one embodiment, a second segmentation of the first vessel automatically generates a plurality of segment types including:

[0062] ■ 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;

[0063] ■ 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, each of the sets of segments having a system of equations modeling the hemodynamic flow in said portion.

[0064] According to one embodiment, the second segmentation of the first vessel automatically generates a plurality of segment types including:

[0065] ■ A third segment type characterized by the presence of a local curvature of the vessel greater than a predefined threshold and / or;

[0066] ■ A fourth type segment characterized by local dilation of the vessel (aneurysm).

[0067] ■ 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.

[0068] 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.

[0069] One advantage is to simplify the equations and allow easier training by reducing the dimension of the solver.

[0070] According to one embodiment, the system of equations comprises a second hemodynamic numerical model comprising for each portion of vessel at least one model among which: ■ A mass conservation model and / or;

[0071] ■ A model of conservation of momentum and / or;

[0072] ■ An equation of state for pressure and / or;

[0073] ■ A first model of a pressure delta and / or;

[0074] ■ A second model of a pressure delta established from in-vitro measurements.

[0075] 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.

[0076] 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.

[0077] An advantage is having a semi-empirical model that can be refined for each anatomical profile considered.

[0078] 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.

[0079] One 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.

[0080] 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.

[0081] One advantage is that it simplifies the use of the machine learning model by exploiting only a limited number of input data.

[0082] 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 validation data from pressure measurements at different points of the portion of the vessel considered.

[0083] According to one embodiment, the first high-fidelity block processes as input data from the first set of training data, called in vivo data, and the second low-fidelity block processes as input data from the second set of training data, called CFD data, and data from the third set of training data, called in vitro data.

[0084] 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:

[0085] ■ Acquisition of a first set of training data, called in-vivo data, from: o Acquisition of a first image from an imaging system; o Extraction of a first set of training data defining anatomical descriptors of a first vessel of said first image; o Acquisition of a set of patient data, called patient data, comprising at least the heart rate and the myocardial mass; o Reading of data characterizing pressure measurement points of a first vessel defining test and validation data of a machine learning model;

[0086] ■ Execution of the machine learning model whose inputs include the first training data set and data generated from the patient data and learning by implementing a cost function minimizing the error between data produced by the model and the validation data;

[0087] ■ Acquisition of a second set of training data, called CFD data, from: o Acquisition of a first image from an imaging system; o Extraction of a second set of training data defining anatomical descriptors of a first vessel of said first image; o Resolution of a solver modeling a model of hemodynamic equations from the incompressible Navier Stokes equations in one dimension, the data estimated by the solver defining validation data of a machine learning model;

[0088] ■ Execution of the machine learning model whose inputs include the second training data set and learning by implementing a cost function minimizing the error between data produced by the model and the test and validation data;

[0089] ■ Acquisition of a third set of training data, called in-vitro data, from: o 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; o Execution of a set of fluid flow tests with a variety of different geometries within the test bench; o Measurement of data characterizing pressure measurement points of a first channel portion defining test and validation data for a machine learning model;

[0090] ■ Execution of the machine learning model whose inputs include the third training data set and learning by implementing a cost function minimizing the error between a data produced by the model and the validation data.

[0091] One advantage is having a wide variety of training data to train the model on a wide variety of cases. Another advantage is that different branches or training data can be used to configure another branch. Thus, in vitro data can be used to configure the training branch based on the CFD solver. Similarly, data acquired by imaging real patients can be used to configure the CFD solver.

[0092] According to an alternative or combination embodiment, the training method comprises solving a solver modeling a hemodynamic equation model from the incompressible Navier Stokes equations in three dimensions, the data estimated by the solver defining validation data of a machine learning model.

[0093] According to one embodiment, the first machine learning model of the training method implements a parameterizable loss function including at least one 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.

[0094] According to one embodiment, the first machine learning model of the training method is a DeepONet network.

[0095] According to one embodiment, the first machine learning model is a multi-fidelity model comprising a first high-fidelity block and a second low-fidelity block, each block comprising a first sub-network defining a main branch considering as input the parameters of an input function sampled at specific points and a second sub-network defining a Trunk branch considering as input the coordinates of the specific points where an operator is to be evaluated, the patient data of the first set thus defining the inputs in the main branch of the high-fidelity and low-fidelity blocks, and the patient data of the second set thus defining the inputs in the Trunk branch of the high-fidelity and low-fidelity blocks.

[0096] ■ According to a first configuration, the second low-fidelity block is trained with at least the data of the second set of training data considered in one dimension, called 1D CFD data, and the first high-fidelity block is trained with at least the second set of training data considered in three dimensions, called 3D CFD data;

[0097] ■ According to a second configuration, the second low-fidelity block is trained with at least the data of the second training data set considered in one dimension, called 1D CFD data and the first high-fidelity block is trained with at least the data of the third training data set, called in vitro data,

[0098] ■ According to a third configuration, the second low-fidelity block is trained with at least the data of the second set of training data considered in one dimension, called 1D CFD data and the data of the third set of training data, called in vitro data, and the first high-fidelity block is trained with the second set of training data considered in 3 dimensions, called 3D CFD data,

[0099] ■ According to a fourth configuration, the second low-fidelity block is trained with at least the data of the second training data set considered in one dimension and / or in three dimensions and the data of the third training data set, called in vitro data, and the first high-fidelity block is trained with the data of the first training data set, called in-vivo data,

[0100] ■ According to a fifth configuration, the second low-fidelity block is trained with at least the data of the second training data set considered in one dimension, called 1D CFD data and the data of the third training data set, called in vitro data, and the first high-fidelity block is trained with the data of the second training data set considered in three dimensions, called 3D CFD data and the data of the first training data set, called in-vivo data.

[0101] According to another aspect, the invention relates to a system for estimating the coronary reserve flow fraction of a vessel comprising:

[0102] ■ An electronic device comprising an interface for acquiring at least a first image from an imaging system; ■ Said electronic device further comprising a first computer and a first memory for extracting a first set of data defining anatomical descriptors of a first vessel from said first image;

[0103] ■ Said device comprising a second interface for acquiring a second set of data, called patient data, comprising at least the heart rate and the myocardial mass;

[0104] ■ Said electronic device comprising a second computer and a second memory for generating an input comprising the first data set and the second data set and for generating an output defining a prediction of a quantity of coronary reserve flow fraction by means of the execution of 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.

[0105] According to another aspect, the invention relates to a system for estimating the coronary flow reserve fraction (FFR) of a vessel, an electronic device for implementing the estimation method of the invention or the training method of the invention.

[0106] Brief description of the figures

[0107] Other characteristics and advantages of the invention will emerge on reading the detailed description which follows, with reference to the appended figures, which illustrate:

[0108] ■ Figure 1: a representation of the different systems for acquiring and processing data and images of a patient's vessels to predict the FFR of at least one first vessel;

[0109] ■ Figure 2: a representation of the result of a segmentation step of a 3D artery comprising several vessels with the creation of central lines for each arterial vessel;

[0110] ■ Figure 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;

[0111] ■ Figure 4: a representation of a vessel straightened along an Ox axis making it possible to implement a segmentation step of an embodiment of the method of the invention;

[0112] ■ Figure 5: an embodiment of the main steps of the FFR estimation process;

[0113] ■ Figure 6: an embodiment of the main steps of the method for training a machine learning model according to the invention;

[0114] ■ Figure 7 A: an example of the implementation of an architecture at one output of a DeepONet type network including the implementation of a cost function parameterized according to physical constraints;

[0115] ■ Figure 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;

[0116] ■ Figure 7C: an exemplary embodiment of an architecture of Figure 7B implemented according to the methods of the invention;

[0117] ■ Figure 8: An example of a test bench for performing measurements to define a training dataset containing data to test and validate the machine learning model to collect in vitro data;

[0118] ■ Figure 9: an example of a geometry model that can be used on the test bench in Figure 8;

[0119] ■ Figure 10: other examples of geometry model of a stenotic portion that can be used on the test bench of figure 8, ■ Figure 11: an example of second adapted segmentation implemented to cut different vessels according to types of segments.

[0120] ■ Figure 12: an example of a multi-fidelity model according to the invention,

[0121] ■ Figure 13: the results and performances of a DON type architecture, based on ENSi data called in vitro data and ENSi data called CFD data.

[0122] Definitions

[0123] In the present invention, the term "FFR" refers to a ratio between an inlet pressure of a vessel and an outlet pressure.

[0124] We call "Pa": the inlet pressure of a vessel.

[0125] We call "Pd": the outlet pressure of a vessel.

[0126] We call "Pdi": the pressure along the axis of a vessel.

[0127] We call "ST": a stenosis in the general case and "STi" when a particular stenosis is designated and described in an example.

[0128] A “DON” network is called a DeepONet network, which in English means “Deep Operator Network”.

[0129] A machine learning model trained to generate outputs from input data is called “MLAi”.

[0130] The data needed to train the machine learning model used according to different data sources are called “ENSi'”, “ENSi””, “ENSi'"”.

[0131] ENSi' refers to training data used and measured in vivo. These measurements may involve invasive means to measure pressures upstream and downstream of stenoses.

[0132] “ENSi” refers to training data obtained from a model modeling MOD2 hemodynamic flows. This model can be in 1D or 3D.

[0133] ENSi” refers to training data used and measured in vitro.

[0134] We call "ENSi" the data acquired by the machine learning model when operating the trained model. We note that the data in the ENSi set. We call "ENS2" the "patient data" corresponding to the patient data that can be used to produce E1 input data for the network. These ENS2 data can include heart rate fc, myocardial mass, systolic rate. The data in the ENS2 set can include additional data, such as age, gender of an individual. More generally, the data in the ENS2 set correspond to measured physiological data, demographic data, history, etc., these data define part of the input data of the trained MLA1 machine learning model.

[0135] According to one embodiment, the ENS2 set makes it possible to directly define certain input data E1 of the MLA1 model when they are acquired directly in the form used by the latter. According to another embodiment, the ENS2 set makes it possible to define normalized input data E1 of the MLA1 model by an intermediate calculation. For example, the estimation of the incoming blood flow of a vessel, a flow rate of the hyperemic flow, an elasticity coefficient of a vessel, the basic pressure at equilibrium can be obtained from the ENS2 data.

[0136] We call "ENS2'" the "patient data" to train the MLA1 machine learning model corresponding to the measured physiological data, demographic data, history, etc. We find the data of the same nature as the data previously defined ENS2.

[0137] It is possible in some embodiments that the ENS2 data is used for training the MLA1 model, accordingly, data from the ENS2 set may be included in the ENS2' set.

[0138] The term "CFD" refers to a solver of Navier Stokes differential equations, which in English stands for "computational Fluid Dynamics" meaning numerical analysis of fluid mechanics.

[0139] A one-dimensional Navier Stokes differential equation solver is called "1D CFD".

[0140] We call Lo P é(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(Q). We call L Phy(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 L P hysics(0).

[0141] A "first segmentation" is called SEGi, the segmentation allowing to acquire images from a 3D imaging system and to select a vessel or an artery of interest and to calculate the interior, exterior volumes and to calculate the center lines of the vessels or arteries. This first segmentation is suitable for performing segmentation of DICOM images.

[0142] A "second segmentation" is called SEG2, the segmentation allowing to divide a vessel into several longitudinal portions in order to use a MOD2 hemodynamic equation model to model the blood flow in each of the portions. This second segmentation is suitable for performing a segmentation of vessel portions in a CFD model called MOD2.

[0143] The segmentation used during the training phase with in vitro test data is called the "third segmentation", SEG3. It corresponds to the segmentation of the different portions of the test bench.

[0144] The term "HIS" refers to the hospital information system, which stands for "Hospital Information System" in English. It can also refer to the system for managing electronic patient health records.

[0145] The name "CFS" refers to the cardiac analysis system, whose acronym stands for "Coronary Flow System" in English.

[0146] Resistance is generally denoted R or R2 in 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.

[0147] Impedance is denoted Zc in general 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 capture the influence of pressure waves and the frequency dependence related to heart rate.

[0148] Compliance is denoted by C, and can be expressed as the inverse of elasticity. Elasticity can also be called elastance. It corresponds to the ability of a tissue to return to its initial state after undergoing deformation. Compliance refers to the ability of a vessel to dilate and increase in volume in response to an increase in internal pressure.

[0149] 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.

[0150] 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.

[0151] 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.

[0152] Method for predicting FFR

[0153] The process for predicting FFR involves several steps.

[0154] Figure 5 represents an embodiment of the steps of the method for estimating the FFR.

[0155] - Image acquisition

[0156] 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 English terminology "Digital Imaging and Communications in Medicine". Such a format allows interoperability of the image with different systems. In addition, different data can be associated and recorded with the image, in particular data relating to the patient. Furthermore, the format allows the exploitation of the imaging data so as to carry out operations and display certain parameters.

[0157] This step is denoted ACQi in Figure 5. The corresponding step during the training phase is denoted ACQi in Figure 6.

[0158] According to one embodiment, a coronary CT scanner is implemented to collect images of an individual. Such an imaging system is based on a computed tomography medical imaging system. It is also called a coronary CT angiography and noted in the literature as CTCA designating "Coronary Computed Tomography Angiography" in English terminology. The image produced is obtained using an X-ray machine. The collected data 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 Figure 2. The method of the invention makes it possible to recover clear images of the heart and arteries.

[0159] An advantage of this imaging system is that CTCA is non-invasive, fast, and offers high-resolution images, allowing detailed evaluation of the coronary arteries.

[0160] Figure 1 represents different components of a non-invasive imaging system such as a CTCA.

[0161] Figure 1 represents a first block denoted HIS allowing to collect the 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.

[0162] A second block, called PACS, is used to archive, record, and transmit the acquired medical data. The PACS component includes a data server. A third block, called VIEW, is used to view the acquired images, create the first segmentation, and exploit metadata and data from the first SEGi segmentation.

[0163] A fourth block denoted CFS comprises a calculation unit allowing the first segmentation SEGi to be used as input and the second segmentation SEG2 of said images to be carried out if necessary during the training of the MLA1 machine learning model or during the exploitation of the CFD MOD2 model.

[0164] According to one embodiment, this calculation unit is also used to implement the CFD solver and / or the MLA1 model for the calculation of the FFR.

[0165] According to one embodiment, this calculation unit is configured to generate a “report” type report making it possible to restore the main outputs of the MLA1 model, the acquisition data and the data calculated from the data produced by the MLA1 model. This report can be displayed on a computer display so that an operator or a doctor can consult it.

[0166] Figure 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 one wishes to estimate the FFR, such as the first vessel 10, from the method of the invention.

[0167] Figure 3 shows the first vessel 10 whose image was acquired using an imaging system such as a coronary CT scanner and which was selected from a selection operation performed on the display.

[0168] 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.

[0169] In the remainder of the description, the method applies to the analysis of a vessel 10 selected from a display.

[0170] Figure 3 in this case represents a 2D sectional view of a vessel 10.

[0171] In the case of Figure 3, the first vessel 10 comprises different stenosed portions ST1, ST2 or non-stenosed portions 6 which can be selected using a selector or a method of automatic detection of diameter variations.

[0172] Representation of images

[0173] 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 segment the image.

[0174] 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, a debouching 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.

[0175] Figure 2 illustrates the result of the first segmentation with the creation of centerlines for each arterial vessel. This step is implemented at the VIEW step of Figure 1.

[0176] An initial SEGi segmentation allows images from the imaging system to be collected and the pixels of interest of a vessel or more generally of an organ to be selected.

[0177] 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.

[0178] This first SEGi segmentation allows to select a vessel for example by selecting a group of pixels of interest from an area to be kept. 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.

[0179] 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 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.

[0180] The first SEGi segmentation allows to delineate the outer surface of the vessel and the inner surface of the vessel and to calculate an average centerline of the vessel.

[0181] According to one embodiment, the method of the invention comprises implementing a rectification algorithm for generating a display of the vessel in a 2D representation along an Ox axis which may define, for example, the centerline of the vessel.

[0182] The first SEGi segmentation includes the ability to define a marker along the vessel on the 2D representation or the 3D representation in order to visualize section planes of the vessel. For this purpose, a selector allows a user to select a section plane from a marker.

[0183] 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 MOD2 model known as CFD.

[0184] Representation of the selected vessel

[0185] Figure 4 illustrates a representation of a vessel 10 straightened along an Ox axis. The figure represents different parts of the vessel 10 and different descriptors of the vessel 10.

[0186] 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. In Figure 4 are represented plaques denoted 4 such as calcium plaques in this example which form on the internal 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.

[0187] Preprocessing and extraction of anatomical features

[0188] Anatomical data is used to define part of the input data of the MLAi machine learning model and is also used for training the MLAi model.

[0189] 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.

[0190] The extraction step is denoted EXTi in Figure 5 illustrating the implementation of the method to estimate the FFR. The corresponding step during training is also denoted EXTi in Figure 6.

[0191] The inner diameter is preferably extracted over the entire length of the first vessel 10 using analysis and processing of the acquired images.

[0192] - Curvature

[0193] 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 for determining the curvature as a function of the position x on the longitudinal axis Ox of the representation of the straightened vessel of Figure 4 or of the central axis of the non-straightened vessel.

[0194] The curvature of the vessel can therefore be recorded during this operation so as to be reused later as data to model certain portions of the vessel, for example during the training phase using a MOD2 hemodynamic model. The method makes it possible to annotate the portions having a curvature greater than a given threshold, for example in the second SEG2 segmentation step. This operation is carried out in particular during the second SEG2 segmentation. 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 equations.

[0195] According to one embodiment, the curvature of certain portions of the vessel may be used as input to the MLA1 machine learning model.

[0196] 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.

[0197] During the image processing operation, a function of the radius r(x) can be generated by taking all the rays of the vessel or artery under consideration from an origin position xo to a terminal position xt. The sampling resolution of the function can be defined so as to discretize the set of values ​​on a predefined scale.

[0198] 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.

[0199] - Singularity

[0200] The method of the invention comprises a step of detecting a set of singularities along the vessel 10 considered.

[0201] 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. In the remainder of the description, the case where plaques 4 lead to the formation of one or more ST stenoses will be considered as an example.

[0202] - Stenosis

[0203] Figure 4 represents an example case in which two stenoses ST1 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. Note that Figure 4 represents plates 4 not managing stenoses and others resulting in the formation of ST1 and ST2 stenoses. The method of the invention makes it possible to identify and annotate the presence of stenoses on an image of a vessel.

[0204] In 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.

[0205] 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 their counting along the first vessel 10. The portions of vessel comprising an ST stenosis are indexed and the presence of said ST stenosis can be characterized by a set of positions x s along the Ox axis. The stenoses in Figure 4 are denoted ST1 and ST2.

[0206] 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 stenotic portion can be extracted.

[0207] According to other embodiments, the following parameters may be used to characterize a stenosis:

[0208] - The minimum diameter of the stenosis in mm and / or;

[0209] - The minimum area of ​​the stenosis in mm 2 according to a sectional plan of the vessel and / or;

[0210] - The total volume of the stenosis in mm3 and / or;

[0211] - The maximum degree of coronary stenosis expressed as a percentage of vessel diameter and / or;

[0212] - 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;

[0213] - The curvature of the area corresponding to the stenosis.

[0214] These morphological parameters are for example calculated from the identified singularity such as a plate-type singularity.

[0215] According to one embodiment, the diameter or the internal radius of the vessel 10 at each position of a stenosed portion STi, ST2 can also be calculated. This latter data can supplement, for example, data characterizing the thickness of the stenosis in the method of the invention.

[0216] In the case of Figure 4, two stenoses ST1, ST2 were identified along vessel 10. The first stenosis has a length LSTI and the second stenosis has a length LST2. The radius or diameter in these portions can be noted.

[0217] According to one embodiment, the distance between two stenoses ST1 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 MLA1 model.

[0218] 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. The case is considered in the remainder of the description where a vessel is considered entirely from an inlet point, generally a junction zone with an artery and a distal end defined by a geometric or anatomical marker.

[0219] Figure 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 MOD2 hemodynamic model for which one equation can be associated with non-stenosed portions and another equation can be associated with stenosed portions.

[0220] The pressure curve makes it possible to visualize the evolution of the pressure along the vessel. This curve, although represented in Figure 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 MLA1 machine learning model.

[0221] 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.

[0222] The method of the invention makes it possible to estimate, as shown in Figure 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.

[0223] 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.

[0224] Pressure estimation can also be done using the second CFD model called MOD2 in order to train the MLA1 model with the values ​​estimated by the solver.

[0225] This representation illustrates pressure drops after the presence of a stenosis.

[0226] 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; this is the ENSi' training data, known as "in vivo" data.

[0227] The input of the MLAi machine learning model corresponds to the entire vessel or artery considered such as the one represented in Figure 4. The artery or vessel is a topological unit, going from the inlet to the outlet. 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.

[0228] 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 MLAi 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.

[0229] - Process input data to predict FFR

[0230] The anatomical data defined previously defines part of the input data, denoted ENSi, of the MLAi machine learning model.

[0231] According to one embodiment, the input data of the trained MLAi model comprises a second set of ENS2 data characterizing the individual. The ENS2 data may comprise the input flow rate or the input pressure of one or more vessels or patient data making it possible to deduce these input data such as the heart rate, myocardial mass, age, gender, weight of an individual, etc.

[0232] Input flow rate

[0233] 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. 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

[0234] 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.

[0235] 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.

[0236] Depending on the vessel selection, the blood fraction of the artery supplying said vessel is considered.

[0237] The method of the invention makes it possible to deduce from the selection of the first vessel 10 considered the upstream flow supplying said first vessel 10. There are three main arteries supplying the heart and therefore all the vessels. The 3 arteries are noted LAD, LCX and RCA.

[0238] The first artery, LAD, is the artery called the "Left Anterior Descending Artery" in English terminology and in French: "The Anterior Interventricular Artery". This artery supplies the anterior part of the heart, particularly the left ventricle.

[0239] 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.

[0240] The third RCA artery is the "Right Coronary Artery." It primarily supplies blood to the right ventricle and part of the left ventricle.

[0241] These arteries supply oxygenated blood to different parts of the myocardium. Blood flow in these arteries can be calculated based on known proportions of blood ejection in each artery.

[0242] A relationship allows the resting flow rate in a given vessel to be deduced.

[0243] According to one embodiment, the following relationship can be written:

[0244] Qrest — 2.5 * (Mc 0 75 ) [ml / min],

[0245] According to another embodiment, if only the mass of the left ventricle MC_LV is known, this relationship can be written: Qrest-Lv = 12*((0.7*(fc * Psyst) / 1000)-0.4) * MC_LV / 100 [ml / min], where fc is the heart rate and Psyst is the systolic pressure. This relationship is only valid if the flow rate meets the individual's oxygen demand.

[0246] In the case of characterization of hyperemic flow, a hyperemic flow coefficient khyp can be calculated according to an empirical formula. k h yp = 4.5 - 0.018 * ds + 0.00056 * ds 2 - 0.0000085 * ds 3 with ds: The maximum degree of coronary stenosis expressed as a percentage of vessel diameter.

[0247] The following relationship can be written: Qhyp = Qrest * khyp

[0248] If only the mass of the left ventricle is known, the relationship can be written as Qhyp — Qrest_LV * khyp

[0249] According to one embodiment, the model includes as input only the myocardial mass Mc. According to another embodiment, the model includes as input the myocardial mass and the resting flow rate as input. It is understood that the two inputs Qrest and Mc are highly correlated and therefore only one value can be considered as input to the MLAi model. However, the model can take into account both inputs.

[0250] Patient data

[0251] These data are denoted ENS2 in Figure 5 and ENS2' in Figure 6 for the “in vivo” training data. According to one embodiment, the heart rate fc of the individual is input to the MLA1 model. According to one embodiment, the myocardial mass Mc is input to the MLA1 model. According to another example, input data of the MLA1 model such as the baseline pressure at equilibrium po or the inflow are produced from the heart rate fc of the individual and / or the myocardial mass Mc.

[0252] According to one embodiment, additional data is taken into account with the value of the individual's systolic pressure.

[0253] According to one embodiment, the age of the individual is an input to the MLA1 model. According to one embodiment, the gender of the individual is also an input to the MLA1 model.

[0254] According to one embodiment, the weight and height of the individual are inputs to the MLA1 model. 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.

[0255] Contextual data

[0256] Standardization

[0257] The FFR estimation method 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 Figure 5 and in Figure 6. The normalization step is therefore designated NML in training or in exploitation of the MLAi machine learning model. 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.

[0258] The input data can have different formats depending on the data collected. The NML normalization block therefore allows potentially different transformations to be applied to the measured values.

[0259] 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 unit system.

[0260] According to another embodiment, the NML normalization step comprises a data format upgrade. The NML normalization allows generating the data format allowing the input vector to be processed in the same way as the input vector was used for training according to the different training branches.

[0261] According to one embodiment, a data imputation technique is applied to the input data to fill in missing values.

[0262] The input of the MLAi machine learning model is denoted Ei in Figure 5. The corresponding inputs in Figure 6 during the training phases are denoted ENSi', ENSi”, ENSi”', ENS2'. The test and validation data E2, E3, E4 are used to train the model by correcting the error of a cost function Lf.

[0263] - Release of the MLA model

[0264] The method of the invention implements a machine learning model MLA1 to produce output data denoted Si in Figure 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.

[0265] The predicted pressures are used to infer the FFR function along the axis.

[0266] The corresponding outputs during training are denoted respectively S2, S3 and S4 according to the training branches in Figure 6.

[0267] Among the data produced by the MLA1 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.

[0268] From the pressures produced by the MLA1 model, the method of the invention comprises a step of calculating the FFR, namely the Pd / Pa ratio. This step is represented in Figure 5 illustrating the method for estimating the FFR or the output pressures. This step is also represented in Figure 6 representing the training method.

[0269] According to one embodiment, the flow rate Q is predicted by the MLA1 model at any point x of the vessel and throughout the cardiac cycle, including as a function of time t.

[0270] Finally, the values ​​of the input and output A sections can be generated and the evolution of this A(t) section during the cardiac cycle can also be calculated by the MLA1 model.

[0271] According to one embodiment, the method of the invention comprises a step of processing the data generated by the MLA1 model to produce new values ​​of parameters of interest.

[0272] According to an embodiment corresponding to that of Figure 7C, the values ​​of interest are the basic equilibrium pressure Po, the resistance R and the compliance C and the impedance Zc at the output of the portion considered, that is to say calculated at the output section plane. In Figure 4, this output section plane is the pce plane. In Figure 11, this section plane can be defined at the point(s) OBi, OB2, OB3 or OB4.

[0273] Model

[0274] The invention implements a model for predicting the pressure and other 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 known as a "PINN" network. Such a network is particularly suitable for learning physical laws, particularly non-linear 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 network also denoted as “PIDeepONet”. Such a network is referred to as the MLA1 model in this application. The PIDeepONet network can be used to learn various linear or nonlinear operators and impose physical constraints.

[0275] DeepONet Network

[0276] According to one embodiment, the method of the invention implements a machine learning algorithm MLA1 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 training data, for example data ENS1 ', ENS2', ENS1" and / or ENSi'”.

[0277] In a DON network, the loss function Lf is designed to capture the error between the network's 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's prediction and the true output for various input samples ENSi', ENS2', ENS1", ENS1'”.

[0278] In order to represent the mathematical operator from the data, the DON network allows us to consider two components generally noted "trunk", designating "trunk", and "branch", designating "branch" in Anglo-Saxon terminology. The "trunk" component or branch is noted Bt and the "branch" component or branch is noted Bb in the rest of the description. We also speak of network or subnetwork to designate the components Bt and Bb.

[0279] Figure 7A represents an architecture of a network called in English terminology “Physics informed DeepONet”. This example of DON type architecture is advantageously executed in the method of the invention.

[0280] A physics-informed DeepONet network allows output functions to be consistent with physical constraints by minimizing loss taking into account underlying physical laws.

[0281] This architecture includes inputs {u(xi)}i and {yk(i)}k defining the inputs of two branches Bb and Bt of the network respectively. These two branches form subnetworks.

[0282] Figure 7A shows an example of a one-output architecture.

[0283] According to one embodiment, the methods of the invention implement a multi-output network architecture. Figure 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 k ème output of each group are processed together and produce the k ème solution.

[0284] Figure 7C represents an example of an n-output architecture used in the context of the invention so as to generate different outputs here represented by the pressure P, the flow rate Q, and the section A. 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 MLA1 network. They are therefore obtained indirectly. Figure 7C represents in particular the FFR obtained along the axis of the vessel, the basic equilibrium pressure Po, the impedance Zc, the compliance C and the resistance R. 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.

[0285] The entries {u(xi)}i £ [i ;N] represent N distinct input functions. And for each yk(i) taken on an interval K s [1 ; P], there are P values ​​taken in the domain of the function G(uo)). The generated output is denoted G(uo),y(i)).

[0286] 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 includes all of an individual's input data such as their age, heart rate f c, the myocardial mass Mc, etc. A sample may also correspond in the case of model training to a sample of a case modeled in vitro or simulated from a CFD model to which fictitious / virtual patient data have been assigned. u(xi) is a function restoring the parameters for describing the different anatomies of vessels or portions of vessels defining the anatomical training input data ENSi'. u(xi) is a function for processing the training data ENSi' in order to train the MLAi model. 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 input of the operator. This input is generally a function or a set of values ​​that represent a function.

[0287] As an example, a model architecture can be configured to conveniently divide the feature space, with branch Bb handling geometry-related features, while branch Bt handles all other features.

[0288] Different model architecture design strategies may be used within the scope of the invention.

[0289] A first strategy is called an independent strategy. It allows the use of n independent DeepONet-type models, each DeepONet model producing only one function.

[0290] A second strategy called "Split both" in Anglo-Saxon terminology consists of dividing the outputs of the "branch" network and the "trunk" network into n groups, then the k ème group produces the k ème solution.

[0291] A third "branch splitting" strategy allows the "branch" network to be split and the "trunk" network to be shared.

[0292] A fourth strategy called "Split trunk", in English terminology, called "trunk division", can be adopted to separate the "trunk" network and share the "branch" network.

[0293] Branch Bb learns a representation of the input function. To do this, it can 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.

[0294] This Bb branch allows us to understand the structure and properties of the input function, allowing the network to respond correctly to variations in this input data.

[0295] The Bt branch is designed to process the {yk}k points in the domain for which the operator's output is to be evaluated. The Bt branch produces a representation of these points. This representation is then used to predict the operator's output at these specific points.

[0296] 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.

[0297] The outputs of branches Bb and Bt are combined to produce the final output of the network. This combination can be done in several ways. In one example, the combination is achieved by a dot product. 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's input and output. This separation allows for greater flexibility and accuracy in learning complex operators.

[0298] According to an example implementation, the DON network only includes one branch Bb. Such a network is called in English terminology "unstacked DeepONet". It has the advantage of being less consuming in matrix calculations.

[0299] Using many branch networks can be computationally and memory-intensive. Some branch networks can be merged into a single branch network. This implementation is called an unstacked DeepONet, as opposed to the implementation with multiple independent branch networks called a stacked DeepONet.

[0300] According to an example implementation of a DON network, a network architecture is configured so 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.

[0301] 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 physical constraints in the configuration of the loss function, making it possible to penalize predicted values ​​outside a predefined range of values.

[0302] The chosen architecture depends on a compromise between available resources, computation times and the desired accuracy of the FFR estimation.

[0303] According to some variants, the DeepONet type DON network can be configured with different extensions or variations of the model, notably to form a POD-DeepONet or Fourier-DeepONet network, or even V-DeepONet.

[0304] According to one embodiment, the DON network combines a sub-network model architecture comprising a “branch” type sub-network and a “trunk” type sub-network to process different input sources with a multi-fidelity approach, i.e. implementing a multi-fidelity model.

[0305] Such a combination makes it possible to obtain good precision for certain estimates requiring significant calculations and to obtain rapid estimates for certain estimates which may remain global or approximate.

[0306] The multi-fidelity approach is particularly beneficial for optimization applications because it reduces the need for numerous high-fidelity model evaluations.

[0307] For example, a multi-fidelity model implements regression based on Gaussian processes or nonlinear autoregressive schemes to correlate different fidelity levels.

[0308] According to an exemplary embodiment, an attention-based multi-fidelity machine learning model, denoted AttMulFid, is implemented. This model can be configured to process data from several fidelity levels, for example, high and low resolution, while capitalizing on the representation power of deep networks for regression tasks.

[0309] In one embodiment, a network is configured to incorporate a multi-fidelity approach using the 1D incompressible Navier-Stokes equations as low-fidelity input and the 3D equations as high-fidelity input. An autoencoder is configured to extract geometric features and a low-rank representation of the coronary arteries. Quantifying the uncertainty provides insight into the FFR prediction. In one example, target values ​​for the training phase of the DON network are calculated using a reduced-order 1D computational blood flow model. Then, a machine learning model is trained to learn the relationship between the anatomical features and the FFR value calculated using the CFD model.

[0310] According to one embodiment, a 1D CFD blood flow model is used for training, the data is denoted ENSi”. Several series of in vitro experiments were carried out, in particular for training the network, the data obtained is denoted ENSi'”. An advantage of this data is that it is less expensive than in vivo data due to its rarity or 3D CFD data which is very expensive in terms of computation time.

[0311] The method of the invention has the advantage of considering disparate data sources in a coherent predictive model.

[0312] The method enables an implementation of a deep operator learning approach to the problem of blood flow in elastic arterial vessels with stenoses.

[0313] According to the notations used previously, a model is configured product G(u)(y), where G is a nonlinear operator, a mapping from one space of functions into another, u is an input function, and y is a point in the domain of G(u).

[0314] According to this configuration, the function(s) G outputs the pressure and flow rate, and the input function(s) u represents the geometry-related characteristics and y encompasses all other characteristics. Therefore, the output G(u)(y) can be interpreted as the target value of the characteristics at point y in geometry u.

[0315] As described earlier, a DeepONet network operates with two distinct subnets: the “trunk” and the “branch,” which process the u and y inputs respectively.

[0316] In one embodiment, the DeepONet DON network uses a G operator. Various strategies can be implemented in different embodiments to work with multiple outputs. These have been used to model pressure and flow rate. Post-processing the pressure output provides the fractional flow reserve FFR, which is the variable that is sought to be estimated.

[0317] According to this implementation, the flow output serves auxiliary purposes.

[0318] An advantage of using a multi-fidelity DeepONet type network is to integrate in vitro and / or in-vivo experiments, which represent high-fidelity data, denoted HF. Fluid dynamics simulations correspond in this example to low-fidelity data. Different data configurations associated with the low-fidelity and / or high-fidelity subnetwork are possible according to different embodiments of the invention. Figure 12 represents an example of realization of a deep learning model comprising a multi-fidelity model in which a cascaded architecture is implemented between a high-definition HF_DoN subnetwork and a low-definition LF_DoN subnetwork. This model can be denoted DONMF using the previous notations or DeepFFRMF when the latter is configured to predict the FFR. The notations DeepFFRLF and DeepFFRnr are used to designate the subnetworks of a DeepFFRMF in the case of application of the FFR estimation.

[0319] A first low-fidelity block is denoted LF_DoN, also called LF block, and comprises two sub-networks, a first LF-Bb sub-network of which is of the “Branch” type and a second LF-Bt sub-network of the “Trunk” type. A second high-fidelity block is denoted HF_DoN, also called HF block, and comprises two sub-networks, a first HF-Bb sub-network of which is of the “branch” type and a second LF-Bt sub-network of the “trunk” type.

[0320] We recall that the role of the Branch Bb network is to process the parameters or characteristics of the input function u(x). u(x) is sampled at specific points {xi, X2, ... ,x m} to obtain a vector u. This vector is given as input to the Branch network, which encodes this information into a latent vector. The Branch network therefore captures the global dependence on variations in u(x).

[0321] The role of the Trunk network is to process the y coordinates where the operator is to be evaluated. The y coordinates are directly provided to the Trunk network. This network generates a t representation, which captures the local dependence at the y point. The Trunk network therefore focuses on information specific to the spatial or temporal domain.

[0322] Figure 12 represents an example of implementation of a deep learning model of the DON type, according to one example, a DeepONet network. However, other examples are compatible with the invention.

[0323] The blocks are for example subnetworks of the model. The low-fidelity block LF_DoN is configured to estimate the PLF pressure and the QLF flow rate from training data such as the second training dataset ENS1, called CFD data, and the third training dataset ENST, called in vitro data. The high-fidelity block HF_DoN is configured to estimate the PHF pressure and the QHF flow rate from training data such as the first training dataset ENS1, called in vivo data.

[0324] Different configurations are possible during training to associate the data from the different sets with the two LF_DoN and HF_DoN networks.

[0325] According to a first example (a) of configuration, the LF_DoN network is trained with the 1D CFD data and the HF_DoN network is trained with the 3D CFD data.

[0326] According to a second example (b) of configuration, the LF_DoN network is trained with the 1D CFD data, i.e. the ENS1 data” considered in one dimension and the HF_DoN network is trained with the in vitro data, i.e. the ENS1' data”.

[0327] According to a third example (c) of configuration, the LF_DoN network is trained with the 1D CFD data and the in vitro data, i.e. the ENST data” and the HF_DoN network is trained with the 3D CFD data, i.e. the ENS1 data” considered in 3D.

[0328] According to a fourth (d) configuration example, the LF_DoN network is trained with the 1D CFD data and the in vitro data and the HF_DoN network is trained with the in vivo data.

[0329] According to a fifth (e) configuration example, the LF_DoN network is trained with 1D CFD data and in vitro data and the HF_DoN network is trained with 3D CFD data and in vivo data.

[0330] The two blocks are then connected to produce a final prediction.

[0331] Both high-fidelity and low-fidelity blocks can be parameterized by concatenation. In the latter case, the representations of the two blocks are combined directly before being passed to a common output layer.

[0332] Both high-fidelity and low-fidelity blocks can be parameterized by adaptive weighting. In the latter case, the contributions of LF and HF data are dynamically weighted according to their relevance to the task.

[0333] Both high-fidelity and low-fidelity blocks can be parameterized by a DON network. In the latter case, the architecture of a multi-fidelity network is used to give more importance to the most useful parts of the data or representations.

[0334] According to one embodiment, the two blocks link the LF and HF representations to enable interaction and information transfer.

[0335] In a first example, the HF and LF blocks include a so-called multi-fidelity residual component. In this case, the LF network produces a baseline estimate, and the HF network learns only the necessary residuals or corrections.

[0336] In a second example, both the HF and LF blocks include a progressive transfer component. In this case, the HF network starts with weights or representations initialized from the LF network, reducing the need for intensive training.

[0337] In one example, the core of the model relies on deep layers typical of neural networks such as fully connected layers that can capture the complex non-linear relationships between inputs and outputs.

[0338] According to one embodiment, nonlinear activation functions are implemented such as ReLU, Sigmoid, or hyperbolic tangent functions to model nonlinear relationships.

[0339] In one example, a technique called “Dropout” is implemented to prevent overfitting by regularizing the model.

[0340] In one example, a technique called "Batch Normalization" is implemented to accelerate convergence and stabilize training.

[0341] The output layer is configured to generate a single prediction combining the contributions of the different fidelity levels.

[0342] According to one embodiment, the training of a DeepFFRMF and more generally of a DON is adjusted by means of an alternating optimization with the LF and HF blocks trained successively to stabilize the learning.

[0343] In another case, a transfer learning strategy can be implemented between the two blocks. In the latter case, the parameters learned on the LF block are used as starting points for the HF block. In an example of a DeepFFRMF multi-fidelity model architecture, the second training dataset ENS1”, called CFD data, is used as low-fidelity data, while the training set ENSi’”, called in vitro data, serves as high-fidelity data. This example validates the relevance of using a multi-fidelity network. The test results shown in Figure 13 allow us to conclude that such a network is suitable for predicting FFR from a multi-fidelity network.

[0344] According to one implementation, residual learning is based on input augmentation by leveraging the low-fidelity DeepFFRLF sub-models, called the LF block, and the high-fidelity DeepFFRHF sub-models, called the HF block.

[0345] According to this example, one objective is to predict flow rate and pressure, as well as FFR calculated from pressure, using both LF and HF blocks.

[0346] According to the example of residual learning method and input augmentation learning method are combined to define multi-fidelity learning of DeepONet type network. According to this method, high-fidelity model learns to predict the residual between high-fidelity and low-fidelity outputs.

[0347] The residue can be written: [Math 22]

[0348] According to this method, GHF and GLF are assumed to have similar behaviors. This feature makes it easier to learn their R-difference. In input augmentation, the low-fidelity prediction is used as an additional input to the high-fidelity DeepONet backbone. The R-difference, the residual, is easy to learn. In input augmentation, the low-fidelity prediction is used as an additional input to the high-fidelity DeepONet backbone: where Q is the operator learned by high-fidelity DeepONet.

[0349] Alternatively, learning that takes into account the increase in input when the low-fidelity prediction GLF(U) is added to the high-fidelity DeepONet branch network allows defining the

[0350] Considering the first approach. From equations (x) and (y), the final prediction of the high-fidelity solution is defined as follows:

[0351] LF DeepONet

[0352] GHFWM = G LF (u) y + ^W(y,£J(^)(y))

[0353] LF DeepONet HF DeepONet [Math 25]

[0354] In one example, the training dataset is divided into training and test subsets. This method can be used with ENSi training data, also known as in vitro data, ENSi training data, also known as 1D or 3D CFD data, or ENS1 data, also known as in vivo data.

[0355] The architecture of each model is determined by hyperparameter optimization.

[0356] In order to perform a binary classification where cases in which FFR < 0.8 are considered as the positive ischemia criterion and cases where FFR > 0.8 as negative. The binary classification can be performed based on measures associated with the area under the ROC curve also called AUC, specificity, sensitivity, precision, negative predictive value, F1 score and accuracy.

[0357] The following table represents some performances obtained from a DeepONet network according to the metrics used. In this case, the LF_DoN network is trained with 1D CFD data, i.e., the ENS1” data considered in one dimension and the HF_DoN network is trained with in vitro data, i.e., the ENS1’” data. According to one embodiment, the method of the invention comprises a configuration of the model aimed at identifying the important parameters of the model. The calculation of the importance of the parameters is based on an evaluation method by degrading the performance of the model, for example by performing operations on the values ​​of certain characteristics such as value replacements or value permutations. These operations make it possible to evaluate to what extent the results are affected according to the degradations carried out.

[0358] Figure 13 represents the performance of a multi-fidelity network learned from in vitro and CFD data with the measurements made on the test bench allowing to obtain in vitro data constituting the measurements to be approximated. The objective of such a test is to estimate the multi-fidelity precision and to evaluate the relevance of using such a network.

[0359] Based on the time average of the pressures measured upstream and downstream of the vessel, a step is implemented to calculate their ratio and deduce the FFR in order to verify the regression step during training.

[0360] Figure 13 presents scatter plots and Bland-Altman plots comparing the FFR calculated from in vitro measurements with the FFR predicted from a trained DeepFFRMF network. It is found that the differences between the in vitro FFR and the DeepFFR are -0.0029±0.017 with excellent agreement (r=0.99; p<0.0001). Similar differences with experimental data for the pressure difference, AP (Pprox - Pdist), and pressure variables respectively were 0.9±4 mmHg and 1.2±3.5 mmHg.

[0361] Such performances make it possible to validate the very good performances of a multi-fidelity network and its relevance for estimating the FFR by considering different data sources.

[0362] According to an exemplary embodiment, the non-geometric parameters, such as the average inlet flow rate, the basic equilibrium pressure po, the specific impedance representing the resistance of the system, have a significant importance with respect to the other parameters.

[0363] Furthermore, it can be seen that density, viscosity and elasticity can also have substantial importance compared to other parameters, especially some geometric parameters. The multi-fidelity DONMF model, also called DeepFFRiviF, presents very good performances in particular due to the diversity of data sources considered. The advantages of the multi-fidelity approach is to compensate for the limited amount of high-fidelity data, generally in-vivo data.

[0364] Loss functions

[0365] According to an example, the loss function Lf(0) of the DON network is configured to minimize a first term denoted L O pe(0) which corresponds to the loss function of the operator and a second term noted L P hy(9) which corresponds to the loss function of physical constraints.

[0366] 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 L P hy(0) optimizing the error of a system of equations defining bounds and a compatible domain of the physics induced by the Navier Stokes equations.

[0367] The step of calculating and optimizing the error calculated by the loss function is represented in Figure 6 during the training of the MLAi model.

[0368] The loss function can be written: Lf(0) = Lo P é(0) + L P hy(0)

[0369] With, for example, the following expression of the two operators: , ath 3]

[0370] Where {u®}i=i to N denotes N distinct input functions.

[0371] Where {yk(i)}k=i at Q denotes a set of randomly sampled points in the domain G(u( ).

[0372] Where N is a linear or non-linear operator that gives the differential equations the following form: N(u, G) = 0 The physical constraints taken into account in equation [3] by the operator L P hy(9) can take the form of the system of differential equations resulting from the incompressible Navier Stokes equations.

[0373] This system of equations takes the form of a numerical model of hemodynamic equations called MOD1. It can be expressed as follows: [Math 4]

[0374] According to another embodiment, another system of hemodynamic equations can be used to define the MODi model or other equations can be integrated into the MODi model of the equations [4]. These hemodynamic equations can be modeled in 1D, 2D or 3D. Other equations of state than that of pressure can also be used. According to one embodiment, the empirical equation for calculating Young's modulus is used as described for CFD.

[0375] In one example, the Navier Stokes equations are represented in a dimensionless manner and are integrated over the cross-sectional area of ​​the vessel or portion of the vessel under consideration. The parameters and variables are defined as follows:

[0376] [Math 5] 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, 5 is the boundary of the layer thickness and v is viscosity.

[0377] In these equations, a new variable Re, denoting the Reynolds number, is introduced. The values ​​of the variables in a one-dimensional 1D model are considered to be their known maximum values.

[0378] According to different embodiments, methods of optimization and minimization of each equation [4] of the described MODi model can be implemented to solve the system according to a residue or an error to be minimized.

[0379] Model training

[0380] The invention also relates to a method for training the MLAi 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 MLA1 model.

[0381] Figure 6 represents the MLA1 model during these different training phases noted B1, B2, B3 allowing to obtain three inputs of the network to train it. Three inputs are represented in Figure 6 by the blocks Bi, 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.

[0382] An advantage of training using different configurations is to obtain better predictions in the exploitation phase of the MLA1 model.

[0383] Indeed, the first input aims to train the MLA1 model with ENS1' training data tested in vivo, i.e. with patients for whom pressure measurements are made from a catheter. The second input aims to train the MLA1 model with a CFD solver allowing to solve a system of incompressible differential equations of Navier Stockes, these are the ENS1' data. The third branch aims to train the MLA1 model with data measured on a test bench, the measurements are called in vitro, these are the ENSi' data. Such a 3-phase training allows to obtain an exhaustive panel of test data allowing to obtain data representative of the real case, taking into account the physics equations and finally allowing to model a large number of different geometries of stenoses.

[0384] According to one embodiment, the method of the invention may comprise training based solely on a single input {Bi}, {B2} or {B3}, or on two inputs {Bi, B2}, {B1, B3}, {B2, B3} out of three. For example, according to one embodiment, the method of the invention only comprises the training data {ENS1”, E3} and {ENS1'”, E4}. In this case the model is trained solely with data from the CFD solver and in vitro data.

[0385] When the training method includes the first input B1, in vivo tests can be conducted 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.

[0386] Such training comprising data from several inputs B1, B2 and B3 as represented in Figure 6 makes it possible to obtain better predictions of input pressure p a of a first vessel 10 and better pressure predictions on the axis up to the vessel exit including the exit 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.

[0387] Input B2: CFD solver training data

[0388] A second input denoted “cfd” in Figure 6 is used to train the MLA1 machine learning model. According to one embodiment, a training data set corresponding to the test and validation data E3 is obtained by solving a so-called “CFD 1D” model.

[0389] The 1D CFD equation system is for example applied to data acquired from a vessel geometry obtained from an imaging system. Figure 6 represents this example case in which the anatomical data of the vessel 10 from the first segmentation SEG1 of the first input B1 are used to provide anatomical data to the 1D CFD solver of the input B2. Arrow 19 represents the acquisition of these data.

[0390] - Second and third Segmentations SEG2, SEG3 for the CFD solver

[0391] The method of the invention comprises a second segmentation SEG2 of the first vessel 10 into different segments or portions. This step is denoted SEG2 in Figure 6. The second segmentation step SEG2 is used in particular during the training phase in conjunction with the MOD2 modeling model of the hemodynamic flow also called CFD.

[0392] 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 Figure 6 named “in vitro”.

[0393] The third segmentation refers to a pipeline modeled on a test bench comprising portions within which a flow is injected and parameters characterizing the flow are measured. These data can then be used to train the MLA1 model. The third segmentation aims to characterize portions of pipelines having topological properties representing the different singularities of a vessel.

[0394] To this end, the training method of the invention makes it possible to automatically generate sectional planes of the vessel in order to consider each segment as a portion of vessel whose blood flow properties can be calculated using the MOD2 hemodynamic model. One advantage is to calculate test values ​​to train the machine learning model.

[0395] 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.

[0396] Figure 4 also represents different cutting planes generated in particular during the second segmentation SEG2. These cutting planes are noted pci, pc2, pcs, pc4 pcs, pce in Figure 4. They are generated to delimit the different types of portions in the second segmentation. Figure 4 represents different portions including a type of non-stenosed portion 6 and a type of stenosed portion STi, ST2.

[0397] In the example of figure 4, the delimitation planes pci and pc2 delimit a first non-stenosed portion 6, the planes pc2 and pcs delimit a first stenosed portion ST 1, the planes pcs and pc4 delimit a second non-stenosed portion 6 and the section planes pc4 and pcs delimit a second stenosed portion ST2 and finally the section planes pcs and pc4 delimit a third non-stenosed portion 6.

[0398] The section planes are shown in Figure 4 to illustrate that after the PC3 or PCs section plane delimiting the end of a stenotic portion, a pressure drop may be a consequence.

[0399] During training, the use of the MOD2 hemodynamic model in the CFD branch of Figure 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.

[0400] According to one embodiment, when using the MOD2 hemodynamic model, 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.

[0401] Figure 11 shows an example of a second segmentation SEG2 used to generate training data from a MOD2 eigenhemodynamic equation model. In this model, different equations can be applied to different types of portions having a eigenhemodynamic equation model.

[0402] Figure 11 represents a case of modeling several vessels with different bifurcations AB1, AB2 and AB3 representing areas of connection between vessels.

[0403] An inlet of the blood flow is represented by the element IB1 and the different outlets of the blood flow are denoted OB1 , OB2, OB3 and OB .

[0404] A first type of segments sgi, sgs, sg4, sge, sgs, sgg, sgw, sgn, sg, sgu, sgie, sgi7, sg, sg2i, 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], allowing the flow to be modeled and the pressures within the vessel(s) to be calculated by considering initial hypotheses on the flow of the flow.

[0405] According to one embodiment, the method of the invention is carried out for each branch from the entry point I Bi 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.

[0406] According to one embodiment, a mesh is defined to model and solve the system. The number of cells in the mesh along the vessel axis and the time step are two control parameters. Other control parameters can be defined.

[0407] A second type of segments sgs, sg?, sgi2, sg2o corresponds to the portions of the 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

[0021] 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.

[0408] A third type of segments sg2, sg corresponds to 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 an uncurved portion. In this case, an additional equation can be used to model the blood flow by considering initial assumptions on the flow flow.

[0409] A fourth type of sgis segments corresponds to the portions of vessel presenting an aneurysm, that is to say the portions presenting a local bulge of the vessel diameter 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 diameter of the vessel or of the diameter in an adjacent portion. The threshold can also be characterized by the local variation of the diameter. The portions comprising a local bulge can be better modeled by imposing the use of a dedicated flow circulation model which is different from the model used for the circulation in a portion of the first type for example. In this case, a semi-empirical equation similar to the equation

[0021] described below dedicated can be used to model the blood flow by considering initial hypotheses

[0410] Thus, the second segmentation operation is carried out automatically by first labeling the different portions of the vessel according to their own geometric characteristics.

[0411] 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 mean radius, the maximum radius or the local mean 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 mean radius, the maximum radius or the local mean radius after the increase, a cutting plane can be generated.

[0412] - Continuity conditions at the boundaries of segmented portions

[0413] 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 MOD2 models 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.

[0414] Thus, it is possible to train the MLA1 model by the estimated values ​​of the second hemodynamic flow model MOD2 within the training method of the invention by a step-by-step approach. For this purpose, a feedback loop can be used to integrate the values ​​calculated by the application of the second hemodynamic model MOD2 on a plurality of segments linked together with the continuity conditions.

[0415] For the stenosed portions, a mathematical method can be implemented to manage the boundary conditions. For example, a so-called "ghost cells" method can be implemented. These ghost cells are added to the mesh cells.

[0416] 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.

[0417] 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. Ghost cells allow boundary conditions to be defined on 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.

[0418] When integrating the equations on each branch from the entry point IB1 to the different exit points, stenosed or not, the boundary conditions given by the resolution of the Windkessel equations

[0017] at the output, that is to say in the case of figure 11, at points OB1, OB2, OB3 or OB4, make it possible to solve the equations from close to close.

[0419] Figure 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.

[0420] The different geometry segmentations created in vitro can be used as many different scenarios for MOD2, or CFD, modeling. One advantage is that they produce a large amount of training data to cover many scenarios. For example, cases in which several stenosed portions follow one another in the same vessel.

[0421] Furthermore, these geometry data from the 3rd SEG3 segmentation allow the validation of CFD models. Thus, the choice of equations, in particular equation

[0021] for the stenosed portions or equivalent semi-empirical equations, can be adjusted to model certain vessel portions. For example, the coefficients kv and kï of equation

[0021] can be adjusted according to the different geometries of stenosed portions or other coefficients can be calculated and adjusted for other semi-empirical equations.

[0422] In another case, the data are obtained from vessel data already stored in a memory. The data source is denoted PROD1 in Figure 6. The geometric data are denoted E1”. In an example case, the geometric data come from the same images as the in-vivo data from input B1 in Figure 6. One interest is to allow comparing the CFD predictions with the in-vivo measured data.

[0423] The 1D CFD model is obtained by applying the Navier-Stokes equations for each segmented portion or group of portions of the first vessel 10. th 8] 9] , [Math 10]

[0424] 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, 5 is the thickness of the boundary of the layer wall and v is viscosity.

[0425] Equations (6) and (7) can be derived with an assumption of uniform pressure within a section of the vessel.

[0426] According to one embodiment, the speed profile is noted here u and can be expressed as follows: [Math 1 1]

[0427] According to one embodiment, additional terms, such as gravity, may be included in the equations or different velocity profiles.

[0428] According to one embodiment, an equation of state that relates pressure and vessel cross-sectional area may also be added to the system.

[0429] O 14]

[0430] With the following definitions of the constants or parameters taken into consideration: , [Math 15] po and ro are the pressure and radius of the vessel at equilibrium E is the Young's modulus. h is the thickness of the vessel.

[0431] According to one embodiment, the experimental data give the following relationship allowing these latter parameters to be linked: , [Math 16]

[0432] Where ki = 2 10 7 g / (s 2 cm) k2 = 22.53 cm-1 k3 = 8.65-10 5 g / (s 2 cm)

[0433] Relation (16) may, in some embodiments, incorporate elasticity effects such as viscoelasticity without affecting the structure of the CFD solver.

[0434] 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 individual profile parameters.

[0435] The data from the ENS2' set used in the CFD data can be considered in some way as virtual patient data. The input parameters can typically be the pressure po, the inflow but also elasticity coefficients of the vessels, the propagation speed of the pressure wave PWV, etc. The invention can in a certain mode make it possible to define a virtual patient having a heart rate fc, a myocardial mass Mc, an age or a gender, from the input parameters of the model. This correspondence makes it possible to use data from different sources.

[0436] Indeed, there are models that allow to deduce from a heart rate fc, a systolic rate, a myocardial mass Mc, an age or a gender of an individual a basic pressure at equilibrium po and / or the inflow and / or the elasticity of the vessel and / or the propagation velocity of the pressure wave PWV and vice versa. These data can define the input Ei of the MLAi network / model.

[0437] According to one embodiment, the thickness of the vessel considered is taken into account in the elasticity model of the vessels.

[0438] The boundary conditions allow us to solve equations [6] to

[0016] . The boundary conditions are given at the entrance and exit of the vessel considered.

[0439] Boundary conditions can be obtained directly or deduced indirectly from experimental measurements.

[0440] According to one embodiment, among the values ​​which are used for the boundary conditions, we find the resistance Ri or the characteristic impedance Zc, the resistance R2 and the compliance C.

[0441] The outlet conditions can be obtained from the 3-component Windkessel equation. The latter is written as a function of the pressure p and flow q parameters: , [Math 18]

[0442] This equation is true for:

[0443] - the impedance Zc, noted Ri in equation

[0017] ;

[0444] - the following equality: R = Ri + R2 . Different ways can be used to determine the coefficients of resistance R (or R2) and compliance C and impedance Ri or Zc,

[0445] 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.

[0446] The impedance Ri and the compliance C can be obtained for example from the following equations: [Math 19] 20]

[0447] According to another example, values ​​of constants Ri, R2 and C can be considered according to the values ​​published in the literature.

[0448] However, these methods do not allow for adjusting and adapting values ​​to each individual.

[0449] Thus, training the machine learning model allows learning the learning function from the in-vivo measured data and the CFD model.

[0450] The invention allows in a second step, when the machine learning model has been trained, to deduce these values ​​from the application of the MLA1 machine learning model with operating data coming from the ENS1 data set.

[0451] Equations [6] to

[0016] with the boundary conditions given by the Windkessel model

[0017] allow the 1D CFD solver to be solved for vessel branches not having stenosis or more generally not being obstructed.

[0452] For portions with a stenosis, bifurcation, or aneurysm, a semi-empirical equation can be used and solved.

[0453] For example, in the case of stenosis, according to one embodiment, a semi-empirical model expressing a pressure delta, available in the literature, can be used: where Kv and Kt are the viscous and turbulent resistance coefficients, and the subscripts so and si refer to the values ​​immediately before the stenosis and inside the stenosis, respectively.

[0454] Such a model is called the first pressure delta model.

[0455] In this example, we consider that the cross-section is constant along the 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.

[0456] 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 time t.

[0457] The precise expressions of the coefficients K v and Kt can be obtained experimentally or the data can be obtained from the scientific literature.

[0458] Equation

[0021] can be modified for each profile of Figure 10 according to experimental tests. For this purpose the test bench of Figure 8 can be used to reproduce a flow environment close to a vessel under given flow conditions.

[0459] For this, each portion of vessel can be characterized by its type: simple portion, curved portion, portion with a narrowing, or even a portion with a dilation.

[0460] In each of these portions, a pressure delta can be measured by an experimental method using sensors.

[0461] 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 allowing the estimation of the flow characteristics of a fluid to subsequently estimate the coefficients kv and kT.

[0462] A method for estimating these coefficients can be based on the implementation of a machine learning model making it possible to learn the coefficients from a plurality of measurements for which the values ​​characterizing the flow of the fluid are known due to the test bench.

[0463] Equations [6] to

[0015] 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 Figure 11.

[0464] 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, diameter, type, neighboring segments with which it interacts, etc.

[0465] If the system of the vessel(s) being modeled includes one or more bifurcation points, the entire computational area is divided into "branches", each branch consisting of a continuous set of segments between the segments containing the inlet or bifurcation and the outlet boundaries. An example of a bifurcation is shown in Figure 11 at the junction points ABi, AB2, AB3.

[0466] The values ​​of the characteristic parameters of the stenotic portions are solved from equation

[0021] ,

[0467] Appropriate equations such as equation

[0021] are used in "special" segments, e.g., a segment with a stenosis, etc. The 1D CFD model is designed to be readily 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

[0015] , e.g., various treatments of elasticity

[0012] and

[0015] , velocity profile

[0011] or boundary conditions

[0017] ,

[0468] The resolution of the system makes it possible to provide the data to test the MLA1 model during training and to validate the latter to obtain a prediction with a sufficient confidence score. A data normalization step can be carried out, noted NML in Figure 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.

[0469] The normalization step in training from simulations of the second MOD2 model, called CFD modeling, is also used to improve stability by ensuring that all primary variables have comparable magnitudes.

[0470] Entry B3: Training with in vitro measurements

[0471] A third input B3 denoted "In vitro" in Figure 6 is used to train the MLA1 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 allowing thousands of experiments reflecting different configurations to be carried out 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, and the elasticity, for example, from a tensile test.

[0472] Many parameters can be adjusted, such as resistance R, impedance Zc, compliance C and for example the following parameters:

[0473] ■ The radius of the 3D printed artery, expressed in cm

[0474] ■ the length of the segment, expressed in cm

[0475] ■ the maximum speed noted Up, expressed in cm / s

[0476] ■ the pulsation noted f or f c expressed in Hz / 60

[0477] ■ the flow rate Q, expressed in ml / min

[0478] ■ viscosity, expressed in Pa*s

[0479] ■ the density expressed in kg / m 3

[0480] ■ the Reynolds number noted Re

[0481] ■ the equilibrium pressure noted Po and expressed in mmHg ■ the elasticity noted E, and expressed in Mpa or the compliance C which is linked to the elasticity value

[0482] ■ the gravity vector

[0483] Certain parameters allow you to define the Ei input of the network, in particular the ENS2' patient data.

[0484] 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 casting the part, and their configuration or arrangement between them or within the bench.

[0485] An example of a test bench 20 modeling the flow of fluid within different portions is shown in Figure 8. Such a representation is illustrated as an example; other examples of test benches may 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 may correspond to a third segmentation SEG3 which may, for example, imitate or not specific cases of in vivo vessels.

[0486] Figure 8 represents a schematic of the experimental flow loop that allows extensive physiological control of various flow and geometric parameters, including regulated variable flow waveforms, elasticity of all segments, flow resistance, and base pressure.

[0487] The test bench 20 may comprise a pump 21, a reservoir chamber 26, denoted CHR, an inlet 22, a main flow channel 25, a test section 23, a return flow channel 27, a pump 21, pressure sensors 24, flow sensors 28, denoted q(t), Qc(t) and electric valves 29, denoted Rc.

[0488] During such tests, the pressure sensors 24 make it possible to record inlet and outlet pressures for portions to be tested having different geometries.

[0489] Portion 33 is used to test for canal narrowing and is intended to model stenosis.

[0490] Figure 8 further shows a detailed TEST_S test area. The flow direction is indicated with the arrows FL1. A computer-controlled vane pump 21 with an interface based on an electronic card was used to drive the flow using a custom computer program f generating peripheral and coronary inflow profiles with different heart rates.

[0491] Replaceable test sections, e.g., straight with / without stenosis, conical, curved and bifurcations with different angles, can be connected using the associated plumbing near the pressure sensors. The return pipe segment contains an additional pressure control sensor, an electromagnetic flow meter and an electric valve to measure and control systemic flow parameters including Rc, Pc, Qc. The design of the flow loop allows for varying the settings of the resistance valve Rc and the base pressure PO for the CHR reservoir chamber.

[0492] These parameters are adjusted to obtain the desired pressure and flow waveforms for each series of experiments. Pressure transducers P prox and Pdist of high precision (1-2%) and high sensitivity (5uV / V / mmHg), generally used for monitoring proximal and distal blood pressure, can be used upstream and downstream of the test section noted TEST_S in Figure 8. The test section TEST_S includes the portion under test defining a deformation of the section, or at least its narrowing according to a given profile, in order to test different forms of stenosis. This section has a length L. This section is preceded by a segment SEG1 and is continued by a segment SEG2.

[0493] The pressure sensor test system / simulator provides flexible calibration capability. It is also used as an additional method to confirm the accuracy of the entire instrumentation system, including cables and transducers. An ultrasonic flow meter can be used upstream of the test section in conjunction with a device to measure flow and velocity waveforms throughout the test section.

[0494] Figure 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.

[0495] Figure 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 kï of equation

[0021] according to the topology of the singularities describing a stenosis likely to be present in a vessel.

[0496] Narrowing profiles are noted such that the P profile defines a narrowing along straight lines. An S20 profile defines a narrowing along curved lines. An Si 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 and lower part of the vessel. The PU2 profile also has an asymmetry and an induced orientation of the flow along an axis non-collinear with that of the vessel.It is possible to use two profiles from Figure 10 to simulate a case in which two or more stenoses are present as in the case of Figure 4.

[0497] The geometric data thus modeled can be used to produce numerous scenarios. The source of this data is noted PROD2 in Figure 6. The PROD2 source corresponds to the production of the input anatomical descriptors used to define the ENSi'” input data of the MLA1 model.

[0498] As in the CFD framework, the PROD2 component allows the production of geometric data and data from all in-vitro measurements Q, P, A from the sensors placed on the test bench 20.

[0499] According to one embodiment, when training the MLA1 machine learning model, pressure and flow rate measurements at different points in the test channel may be measured using appropriate sensors, including pressure sensors. These values ​​are used to train the model.

[0500] During training, according to one embodiment, it is possible to measure the values ​​of the following parameters at several points in the channel:

[0501] ■ 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

[0502] ■ A(t) at different points, for example 5 to 10 points.

[0503] In addition, the basic 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.

[0504] It is therefore possible to test the values ​​predicted by the MLAi learning model using the measured values.

[0505] The measured data define the E4 data shown in Figure 6. The E4 data allows to test the model during supervised training and to validate the MLA1 machine learning model 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.

[0506] The geometric data and measured data are denoted ENSi'” and E4 in Figure 6. The geometric data are defined to be normalized identically to the training data E or E1” or the operating dataset E1 of the MLA1 model.

[0507] This normalization step is denoted NML. This normalization step allows in particular the processing of multi-fidelity training data coming from different systems.

[0508] Entry B1: Training with in vivo measurements

[0509] A first input B1 and noted "In-vivo" in Figure 6 allows the MLA1 machine learning model to be trained using data 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 comes from living beings, more specifically from humans. The ENS2' patient data used are recorded in a memory before use.

[0510] The method includes a training phase of the MLA1 machine learning model using in-vivo measurements. These data are denoted ENS1'. The measurements can be made 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 taken at different times in the cardiac cycle and with different heart rates. In addition, the in-vivo flow can be measured by different methods, including Doppler ultrasound, thermodilution, etc.

[0511] Patient data relating to heart rate fc, myocardial mass Mc, systolic pressure, patient age, patient gender and all considered patient data obtained in in-vivo measurements are used to produce the ENS2' input data of the E1 input of the MLA1 model, such as inflow or steady-state baseline pressure. In order to produce these ENS2' input data, models for defining normalized E1 inputs are used. An example of a model is the one for deducing the resting inflow Qrest from at least the heart rate f c , systolic pressure Psyst and myocardial mass Mc.

[0512] For example, a patient's age can be used to generate or consolidate a measured value of an equilibrium pressure po or an elasticity coefficient.

[0513] According to one embodiment, this in-vivo data is used during model training to train the HF sub-network in a multi-fidelity approach.

[0514] In 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.

[0515] Laboratory measurements, including hematocrit and protein, can be used, for example, to estimate viscosity.

[0516] Alternatively, the training method of the invention does not include the measurement step, but only a step of reading data already acquired and recorded in a memory.

[0517] The collected dataset can then be used to train an MLA1 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 non-stenotic and stenotic portions are identified as described previously in the FFR estimation process.

[0518] The training data, for the in vivo case, in this case comprise the E2 test data represented in Figure 6. According to one embodiment, the training data comprise on the one hand the ENS1' data extracted from the anatomical descriptors and the ENS2' data called patient data as well as the E2 measured data making it possible to validate the predictions made by the MLA1 model.

[0519] The training data can be split into different groups for testing to define supervised training and to validate the model to obtain a sufficient confidence score.

[0520] The multi-fidelity approach allows combining high-fidelity data that are accurate but expensive to obtain, for example, using in-vitro, in-vivo tests, and low-fidelity data that are less accurate but less expensive, such as the CFD solver, to improve the prediction accuracy.

[0521] The multi-fidelity 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 different fidelity levels.

[0522] List of equations [Math n]

[0523] [1]: Function model of a DeepONet or “Physic informed DeepONet” type machine learning model;

[0524] [2]: equation of a loss function specific to the modeling of the loss reduction linked to the mathematical operator;

[0525] [3]: equation of a loss function specific to the modeling of the loss reduction linked to the mathematical operator;

[0526] [4]; Navier Stokes equations defining the MOD1 model to constrain the loss function of the MLA1 learning model;

[0527] [5]; standardized expressions of the different variables / parameters of the equations [4]; [6]: Navier Stokes mass conservation equation defining the second MOD2 model also called CFD model or CFD solver;

[0528] [7]: Navier Stokes motion conservation equation defining the second MOD2 model also called CFD model or CFD solver;

[0529] [8]: equation allowing the estimated values ​​to be normalized, in particular the section, position and thickness of the wall;

[0530] [9]: equation allowing the estimated values ​​to be normalized, in particular for time and pressure, and in particular in equations

[0061] and

[0072] ;

[0531]

[0010] : expression of the Reynods number;

[0532]

[0011] : equation describing the speed profile;

[0533]

[0012] : pressure equation of state;

[0534]

[0013] : normalized expression of the radius of the vessel at equilibrium;

[0535]

[0014] normalized expression of Young's modulus notably used in equation [7]

[0536]

[0015] : Equation of the section of the vessel at equilibrium;

[0537]

[0016] : Empirical equation for calculating Young's modulus;

[0538]

[0017] : 3-component Windkessel equation;

[0539]

[0018] : normalized expression of the resistance and impedance coefficients of equation

[0017] ;

[0540]

[0019] : expression of the impedance from a measurement of the propagation speed of a pressure wave;

[0541]

[0020] : expression of compliance from a measurement of the propagation speed of a pressure wave;

[0542]

[0021] : semi-empirical equation modeling the flow within a stenosed portion;

[0543]

[0022] : equation of the residue;

[0544]

[0023] : equation of the additional input of the main network of DONHF OR DeepONetHF;

[0545]

[0024] : alternative equation of the additional input of the main network of DONHF OR DeepONetHF;

[0546]

[0025] : equation of the final prediction of the high-fidelity solution.

Claims

CLAIMS 1. Method for estimating the coronary flow reserve fraction (FFR) of a vessel comprising: ■ Acquisition (ACQi) of at least one first image (IMi) from an imaging system; ■ Extraction (EXTi) of a first data set (ENSi) defining anatomical descriptors of a first vessel (10) of said first image (IMi); ■ Acquisition (ACQ2) of a second set of data (ENS2), called patient data, including at least the heart rate (f c ) and myocardial mass (Mc); ■ Generation of an input (E1) comprising the first set (ENS1) of data and data generated from the second set of data (ENS2); ■ Generation (GEN1) 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 (MLA1) and the input (E1), said first machine learning model (MLA1) 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 (MLA1), said parameterized physical constraint resulting in particular from a first numerical model of hemodynamic equations (MOD1).

2. Method according to claim 1 characterized in that the extraction of the first set of data (ENS1) 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.

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), the anatomical descriptors include: ■ at least one first descriptor comprises data characteristic of the radius or diameter of the section in each position of the first vessel (10) and / or; ■ at least one second descriptor comprises 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, STi, ST2), the second descriptor further comprising 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). ■ A third descriptor corresponding to the local curvature of the vessel and / or; ■ A fourth descriptor corresponding to the length of a stenosis (ST, ST1, ST2) and / or; ■ A fifth descriptor corresponding to a local dilation of the vessel (aneurysm).

4. Method according to any one of claims 1 to 3, characterized in that it comprises: ■ estimation of the incoming blood flow rate (Qrest) at rest from at least the heart rate (f c ), systolic pressure (Psyst) and myocardial mass (Mc), the second data set (ENS2) comprising the value of said incoming blood flow rate (Qrest) and / or; ■ estimation of the flow rate of the incoming hyperemic flow at rest from at least the heart rate (f c ), systolic pressure (Psyst) and myocardial mass (Mc), the second data set (ENS2) comprising the value of said incoming hyperemic flow rate.

5. Method according to any one of claims 1 to 4, characterized in that the second set (ENS2) of patient data comprises in particular: ■ An age of the individual; ■ A gender of the individual and / or; ■ An indicator of the individual's diabetes and / or; ■ An indicator of the individual's hypertension and / or; ■ A weight of the individual and / or; ■ A size of the individual and / or; ■ Background data such as the existence and number of previous percutaneous coronary intervention(s), the existence and number of myocardial infarctions, quantification of tobacco consumption.

6. Method according to any one of claims 1 to 5 characterized in that the first machine learning model (MLA1) is a DeepONet network whose loss function (Lf) integrates a mathematical operator (Lopé).

7. Method according to any one of claims 1 to 6 characterized in that the first machine learning model (MLA1) is a multi-fidelity model comprising a first high-fidelity block and a second low-fidelity block, each block comprising a first sub-network defining a main branch (Bb) considering as input the parameters of an input function (u(x)) sampled at specific points (yi) and a second sub-network defining a Trunk branch (Bt) considering as input the coordinates of the specific points (yi) where an operator must be evaluated, the patient data of the first set (ENS1) thus defining the inputs in the main branch (Bb) of the high-fidelity and low-fidelity blocks, and the patient data of the second set (ENS2) thus defining the inputs in the Trunk branch (Bt) of the high-fidelity and low-fidelity blocks.

8. Method according to any one of claims 1 to 7 characterized in that the first factor (L P hy) 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 (MODi) 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.

9. Method according to claim 8 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 (MODi) which comprises a system of equations comprising: ■ A model of conservation of mass; ■ A model of conservation of momentum; ■ An equation of state for pressure.

10. Method according to one of the preceding claims, characterized in that it comprises a training step (Bs) carried out from a third set of training data (ENSi”', E4), said third training data (ENSi'”, 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 (MLA1) 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, the third set of training data (ENSi'”) also includes a measurement and calculation for at least one point of each predefined pipeline section: ■ 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); ■ at least one fluid viscosity value; ■ of at least one value of the pressure (Po) at equilibrium.

11. Method according to claim 10 characterized in that it comprises: ■ a characterization of the different portions of the test bench (20), each portion being characterized by a radius of artery to be modeled, a length of artery to be modeled, an elasticity or a compliance (C) and a type of portion; ■ an injection of a fluid into the test bench (20) reproducing a periodic activity relating to the cardiac cycle characterization of the different portions of the test bench (20) from a pump, a clock and a means of recording a pumping frequency.

12. Method according to any one of claims 1 to 11 characterized in that it comprises a training step (B2) carried out from a second set of training data (ENS1”, Es) characterizing the geometry (ENS1”) of portions of vessels obtained from an imaging system, the training of the machine learning model (MLA1) 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 (MOD2) called numerical solver (CFD1), to define test and validation data (E3) of the machine learning model (MLA1), said numerical solver (CFD1) comprising 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.

13. Method according to claim 12 characterized in that a second segmentation (SEG2) of the first vessel (10) automatically generates a plurality of types of segments (6, ST1, 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, ST1, ST2, sgs, sg?, sgi2, sg2o) 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, ■ a third segment type (sg) characterized by the presence of a local curvature of the vessel greater than a predefined threshold and / or; ■ A fourth segment type (sgis) characterized by a local dilation of the vessel (aneurysm) each of the sets of segments having a system of equations modeling the hemodynamic flow in said portion, the first machine learning model (MLA1) is trained by considering the values ​​estimated by the second model (MOD2) integrated over the entire first vessel (10).

14. Method according to claim 13 characterized in that the system of equations comprises a second hemodynamic digital model (MOD2) making it possible to carry out at least one 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 (MOD2) and making it possible to estimate for each portion of vessel of the second type (ST, ST1, ST2) a pressure delta from a pressure delta model comprising a viscous resistance coefficient (kv) and a turbulent resistance coefficient (kï), the second hemodynamic digital model (MOD2) 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 for pressure and / or; A first model of a pressure delta and / or; A second model of a pressure delta established from in vitro measurements.

15. Method according to one of claims 12 to 14 characterized in that the second hemodynamic digital model (MOD2) makes it possible to estimate for each portion of vessel of the second type (ST, ST1, ST2), of the third type (sgis), and / or of the fourth type (sgis) a pressure delta from a pressure delta model comprising a viscous resistance coefficient (kv) and a turbulent resistance coefficient (kï), said coefficients being estimated from tests carried out on an in vitro test bench (20) of one of claims 12 to 14, said measurements carried out on the test bench (20) making it possible to estimate flow characteristics of a fluid.

16. Method according to one of the preceding claims, characterized in that a first set of training data (ENS1', ENS2', E2) comprises geometry data (ENS1') extracted from a patient vessel imaging system, a set of patient training data (ENS2') comprising data generated from at least the heart rate (f c ), systolic pressure (Psyst) and myocardial mass (Mc) and validation data (E2) from pressure measurements at different points of the portion of the vessel considered.

17. Method according to claim 16 characterized in that the second set of patient training data (ENS2') comprises in particular: ■ An age of the individual; ■ A gender of the individual and / or; ■ An indicator of the individual's diabetes and / or; ■ An indicator of the individual's hypertension and / or; ■ A weight of the individual and / or; ■ A size of the individual and / or; ■ Background data such as the existence and number of previous percutaneous coronary intervention(s), the existence and number of myocardial infarctions, quantification of tobacco consumption.

18. Method according to any one of claims 1 to 9 and any one of claims 10 to 11 and according to any one of claims 12 to 15 and according to any one of claims 16 to 17 characterized in that the first high-fidelity block processes as input data from the first training data set (ENSi') called in vivo data and in that the second low-fidelity block processes as input data from the second training data set (ENSi”), called CFD data and data from the third training data set (ENSi'”), called in vitro data.

19. Method for 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 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), said training method comprising: ■ Acquisition of a first set of training data (ENSi', E2), called in vivo data, from: o Acquisition (ACQ1) of a first image (IM1) from an imaging system; o Extraction (EXT1) of a first set of training data (ENSi') defining anatomical descriptors of a first vessel (10) of said first image (IM1); o Acquisition of a set of patient data (ENS2'), called patient data, including at least the heart rate (f c ) and the myocardial mass (Mc); o Reading data (E2) characterizing pressure measurement points of a first vessel (10) defining validation data for a machine learning model (MLA1); ■ Execution of the machine learning model (MLA1) whose inputs include the first training data set (ENS1') and data generated from patient data (ENS2') and learning by implementing a cost function minimizing the error between a data produced (52) by the model (MLA1) and the validation data (E2); ■ Acquisition of a second set of training data (ENS1”, E3), called CFD data, from: o Acquisition (ACQ1) of a first image (IM1) from an imaging system; o Extraction (EXT1) of a second set of training data (ENS1”) defining anatomical descriptors of a first vessel (10) from said first image (IM1); o Resolution of a solver (CFD1) modeling a model (MOD2) of hemodynamic equations from the incompressible Navier Stokes equations in one dimension, the data estimated (E3) by the solver (CFD1) defining validation data of a machine learning model (MLA1); ■ Execution of the machine learning model (MLA1) whose inputs include the second training data set (ENS1”) and learning by implementing a cost function minimizing the error between a data produced (53) by the model (MLA1) and the validation data (E3); ■ Acquisition of a third set of training data (ENSi'”, E4), called in vitro data, from: o 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); o Execution of a set of fluid flow tests with a variety of different geometries within the test bench (20); o Measurement of data (E4) characterizing pressure measurement points of a first channel portion defining validation data for a machine learning model (MLA1); ■ Execution of the machine learning model (MLA1) whose inputs include the third training data set (ENS1'”) and learning by implementing a cost function minimizing the error between a data produced (S4) by the model (MLA1) and the validation data (E4).

20. Method according to claim 19 characterized in that the first machine learning model (MLA1) is a DeepONet network.

21. Method according to any one of claims 19 to 20 characterized in that the first machine learning model (MLA1) is a multi-fidelity model comprising a first high-fidelity block (LF_DoN) and a second low-fidelity block (HF_LoP), each block comprising a first sub-network defining a main branch (Bb) considering as input the parameters of an input function (u(x)) sampled at specific points (yi) and a second sub-network defining a Trunk branch (Bt) considering as input the coordinates of the specific points (yi) where an operator must be evaluated, the patient data of the first set (ENS1) thus defining the inputs in the main branch (Bb) of the high-fidelity and low-fidelity blocks, and the patient data of the second set (ENS2') thus defining the inputs in the Trunk branch (Bt) of the high-fidelity and low-fidelity blocks.

22. Method according to claim 21 characterized in that: ■ According to a first configuration, the second low-fidelity block (LF_DoN) is trained with at least the data of the second set of training data (ENSi”) considered in one dimension, called 1D CFD data, and the first high-fidelity block (HF_DoN) is trained with at least the second set of training data (ENSi”) considered in three dimensions, called 3D CFD data; ■ According to a second configuration, the second low-fidelity block (LF_DoN) is trained with at least the data of the second training data set (ENSi”) considered in one dimension, called 1D CFD data and the first high-fidelity block (HF_DoN) is trained with at least the data of the third training data set (ENSi'”), called in vitro data, ■ According to a third configuration, the second low-fidelity block (LF_DoN) is trained with at least the data of the second training data set (ENSi”) considered in one dimension, called 1D CFD data and the data of the third training data set (ENSi'”), called in vitro data, and the first high-fidelity block (HF_DoN) is trained with the second training data set (ENSi”) considered in 3 dimensions, called 3D CFD data, ■ According to a fourth configuration, the second low-fidelity block (LF_DoN) is trained with at least the data of the second training data set (ENSi”) considered in one dimension and / or in three dimensions and the data of the third training data set (ENSi'”), called in vitro data, and the first high-fidelity block (HF_DoN) is trained with the data of the first training data set (ENS1 '), called in-vivo data, ■ According to a fifth configuration, the second low-fidelity block (LF_DoN) is trained with at least the data of the second training data set (ENSi”) considered in one dimension, called 1D CFD data and the data of the third training data set (ENSi”), called in vitro data, and the first high-fidelity block (HF_DoN) is trained with the data of the second training data set (ENSi”) considered in three dimensions, called 3D CFD data and the data of the first training data set (ENSi’), called in-vivo data.

23. System for estimating the coronary flow reserve fraction (FFR) of a vessel comprising: ■ An electronic device comprising an interface for acquiring (ACQi) at least one first image (IMi) from an imaging system; ■ Said electronic device further comprising a first computer and a first memory for extracting (EXTi) a first set of data (ENSi) defining anatomical descriptors of a first vessel (10) from said first image (IMi); ■ Said device comprising a second interface for acquiring (ACQ2) a second set of data (ENS2), called patient data, comprising at least the heart rate (f c ) and myocardial mass (Mc); ■ Said electronic device comprising a second computer and a second memory for generating an input (E1) comprising the first set (ENSi) of data and the second set of data (ENS2) and for generating 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 (MLA1) to produce an output (Si), said first machine learning model (MLA1) 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 (MLA1), said parameterized physical constraint resulting in particular from a first numerical model of hemodynamic equations (MOD1).

24. System for estimating the coronary flow reserve fraction (FFR) of a vessel an electronic device for implementing the method of one of claims 1 to 18.

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