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

Abstract

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

Description

Title of the invention: COMPUTER-IMPLEMENTED METHOD FOR FRACTION ESTIMATION CORONARY RESERVE FLOW SYSTEM Scope of the invention

[0001] The field of the invention relates to methods and systems for predicting a coronary flow reserve value, known as FFR, for the characterization of coronary flow. More particularly, the field of the invention relates to non-invasive methods implementing software tools for characterizing coronary flow. The invention relates to means that provide decision support for stent placement, invasive investigation of a pathology, or, conversely, ruling out the risk of myocardial infarction, for example. State of the art

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

[0003] One of the most important constants in the evaluation and characterization of coronary flow is coronary flow reserve, also known as FFR, which stands for "Fractional Flow Reserve" in the English-language literature. Generally, FFR measurement with the required precision is performed 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 to characterize the coronary flow of the vessel. Certain FFR values ​​may lead to patient monitoring, further investigations, or even intervention for stent placement.

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

[0005] Other solutions relying solely on a machine learning approach do not allow for optimal training of a model. Indeed, such a model requires training on thousands, or even millions, of data points due to the large number of numerical parameters measured in each patient, corresponding to all the specific characteristics of each patient and all the blood flow configurations within each vessel. This is notably the case with the application published under number FR3096498 and filed on May 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 patient's age, etc.

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

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

[0008] According to one aspect, the invention relates to a method for estimating the fraction of coronary reserve flow of a vessel comprising: • Acquisition of at least one initial image of an imaging system; • Extraction of an initial dataset defining descriptors anatomical features of the first vessel in the said first image; • Acquisition of a second set of data, called patient data, including at least heart rate and myocardial mass; • Generating an input containing the first set of data, the second set of data; • Generation of 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.

[0009] The method advantageously allows for the estimation of pressure at each point in the vessel and thus enables the estimation of the fraction of coronary reserve flow at each point in the vessel. One advantage is obtaining a precise estimate of the fraction of coronary reserve flow, accurately reflecting the specific case of the individual under consideration, without using an invasive measurement. Another advantage of using a cost function incorporating a physical constraint is to improve the performance of the machine learning model, particularly when using heterogeneous training data, i.e., data from different sources.

[0010] According to one embodiment, the extraction of the first data set is obtained through 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 a first vessel displayed on a display, the selection of a point of the vessel.

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

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

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

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

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

[0016] One advantage is to allow the identification of certain parts of the vessel in order to characterize them and to obtain a better estimation of the pressures thanks to the trained machine learning model.

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

[0018] One advantage is having measurable input data for each patient, and taking this into account allows for a better estimation of the output pressure at each point of the first vessel.

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

[0020] One advantage is having measurable input data for each patient, and taking this into account allows for a better estimation of the output pressure at each point of the first vessel.

[0021] According to one embodiment, the second set of patient data includes, in particular: • The individual's age; • A type of individual; • An indicator of an individual's diabetes; • An indicator of an individual's hypertension.

[0022] One advantage is having personalized input data, in particular from data that can be collected simply and which allows for improved prediction of output pressure according to the patient profile.

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

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

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

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

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

[0028] One advantage is to take into account several constraints characterized by different equations of physics and allowing the training domain to be limited.

[0029] According to one embodiment, the method includes 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 test pipe portion and sensors enabling the measurement of test data at different points of said test bench including in particular the flow rate, pressure, viscosity, fluid resistance, Reynolds number and fluid density.

[0030] An advantage of allowing the generation of numerous training data taking into account many anatomical geometries without requiring testing a wide variety of vessel geometries from different patients.

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

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

[0033] One advantage is to allow control of a wide variety of parameters of the in vitro model and to simulate different virtual patients representing a diversity of patients.

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

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

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

[0037] One advantage is having a large training possibility from medical data such as real patient images whose flow values ​​and characteristics can be estimated to train the machine learning model of the invention.

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

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

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

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

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

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

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

[0045] According to one embodiment, the second hemodynamic numerical model allows for the estimation, for each portion of the second type of vessel, of a pressure delta from a pressure delta model comprising a viscous resistance coefficient and a turbulent resistance coefficient.

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

[0047] According to one embodiment, the second hemodynamic numerical model allows for the estimation, for each portion of vessel of the second type, the third type, and / or the fourth type, of 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 allowing for the estimation of flow characteristics of a fluid.

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

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

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

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

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

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

[0054] Other features and advantages of the invention will become apparent from the following detailed description, with reference to the accompanying figures, which illustrate: • [Fig.1]: a representation of the different systems allowing the acquisition and processing of data and images of a patient's vessels to predict the FFR of at least one first vessel; • [Fig. 2]: a representation of the result of a segmentation step of a 3D artery with multiple vessels and the creation of central lines for each arterial vessel; • [Fig. 3]: a representation of a particular vessel that we wish to to estimate the FFR from a segmentation according to an embodiment of the process of the invention; • [Fig. 4]: a representation of a vessel upright along an Ox axis enabling the implementation of a segmentation step of an embodiment of the process of the invention; • [Fig. 5]: a method for carrying out the main steps of the process FFR estimate; • [Fig. 6]: a method of carrying out the main steps of the process training a machine learning model according to the invention; • [Fig.7A]: an example of the implementation of a single-output architecture of a DeepONet type network including the implementation of a cost function parameterized according to physical constraints; • [Fig.7B]: an example of the implementation of a multi-output architecture of a DeepONet type network including the implementation of a cost function parameterized according to physical constraints; • [Fig.7C]: an example of the realization of an architecture of [Fig.7B] implemented according to the processes of the invention; • [Fig. 8]: an example of a test bench for performing measurements define a training dataset containing data to test and validate the machine learning model; • [Fig.9]: an example of a geometry model that can be used on the test bench of the [Fig.8]; • [Fig. 10]: other examples of geometry model of a stenosed portion that can be used on the test bench of [Fig. 8], • [Fig. 11]: an example of adapted second segmentation implemented to cut different vessels according to segment types. Definitions

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

[0056] The term “Pa” refers to the inlet pressure of a vessel.

[0057] The term “Pd” refers to the outlet pressure of a vessel.

[0058] The term "Pdi" refers to the pressure along the axis of a vessel.

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

[0060] A "DON" network is called a DeepONet network, which in Anglo-Saxon terminology means: "Deep Operator Network".

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

[0062] The data required for training the machine learning model used from different data sources are named “ENSi’”, “ENSi””, “ENSi’””

[0063] ENSi' refers to the training data used and measured in vivo.

[0064] ENSi” refers to training data obtained from a model modeling M0D2 hemodynamic flows.

[0065] ENSi” refers to the training data used and measured in vitro.

[0066] The data acquired by the machine learning model during the operation of the trained model are called "ENSi". Note that the data in the ENSi set may include additional data compared to one of the ENSi' or ENSi” sets, in particular "patient data".

[0067] The "patient data" corresponding to the measured physiological data, demographic data, history, etc., are called "ENS2"; these data define part of the input data of the trained MLai machine learning model.

[0068] The "patient data" is named "ENS2'" to train the machine learning model MLai corresponding to the measured physiological data, demographic data, and history.

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

[0070] A Navier-Stokes differential equation solver is called a "CFD," which in Anglo-Saxon terminology stands for "computational Fluid Dynamics," meaning numerical analysis of fluid mechanics.

[0071] A one-dimensional Navier-Stokes differential equation solver is called a "1-D CFD".

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

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

[0074] A "first segmentation" is called SEGi, the segmentation allowing the acquisition of images from a 3D imaging system and the selection of a vessel or artery of interest and the calculation of the internal and external volumes and the calculation of the centerlines of the vessels or arteries.

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

[0076] The hospital information system is referred to as "HIS," the acronym for which stands for "Hospital Information System" in Anglo-Saxon terminology. It can also refer to the system for managing patients' electronic health records.

[0077] The cardiac analysis system is called "CFS", the acronym of which means in Anglo-Saxon terminology "Coronary Flow System".

[0078] Resistance is generally denoted by 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.

[0079] Impedance is generally denoted Zc and Ri in the equations. Impedance allows us to take into account the dynamic aspects of the flow and the vessel, particularly the fact that the vessel contracts and dilates over time within the cardiac cycle. Impedance can also represent the influence of pressure waves and the frequency dependence related to the heart rate.

[0080] 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.

[0081] The values ​​Po, Ao correspond to measured, estimated, or calculated values ​​at equilibrium. In the cardiac cycle, this corresponds to the instant at which the fluid, i.e., the blood, is least subject to dynamic forces. This corresponds, for example, to a local minimum of certain dynamic values, notably velocity or flow rate.

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

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

[0084] The process for predicting the FFR involves several steps.

[0085] Figure 5 represents an embodiment of the steps of the process for estimating the FFR. Image acquisition#

[0086] In one embodiment, a first step involves acquiring at least one image of a set of at least one vessel from an imaging system. In another 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, which in English stands for "Digital Imaging and Communications in Medicine." This format allows for image interoperability with different systems. Furthermore, various data can be associated with and recorded along with the image, including patient data. Moreover, the format allows the imaging data to be used to perform operations and display certain parameters.

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

[0088] According to one embodiment, a coronary CT scanner is used to acquire images of an individual. Such an imaging system is based on a computed tomography (CT) imaging system. It is also called coronary CT angiography and is referred to in the literature as CTCA, which stands for "Coronary Computed Tomography Angiography" in Anglo-Saxon terminology. The image produced is obtained using an X-ray device. 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 [Fig. 2]. The method of the invention makes it possible to obtain clear images of the heart and arteries.

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

[0090] Fig. 1 represents different components of a non-invasive imaging system such as a CTCA.

[0091] Figure 1 represents a first block, labeled HIS, for collecting data measured in a patient by measurement devices, such as imaging data like an MRI image or a coronary CT scan image. This component is also capable of receiving reports or analyses produced by the CFS component.

[0092] A second block, designated PACS, allows for the archiving, recording, and transmission of acquired medical data. The PACS component includes a data server.

[0093] A third block labeled VIEW allows visualization of the acquired images, creation of the first segmentation and exploitation of metadata and data from the first SEGi segmentation.

[0094] A fourth block, denoted CFS, includes a computing unit that allows 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 machine learning model MLAi or during the exploitation of the CFD model M0D2.

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

[0096] According to one embodiment, this computing unit is configured to generate a "report" type output displaying the main outputs of the MLAI model, the acquisition data, and the data calculated from the data produced by the MLAI model. This report can be displayed on a computer screen so that an operator or a physician can consult it.

[0097] Figure 2 shows a segmented 3D view of the aorta and coronary vessels (e.g., LAD, LCX, RCA). A vessel is shown among other vessels. It is hereafter referred to as the "first vessel" and is denoted as 10. The method of the invention allows the selection of a vessel whose FFR one wishes to estimate, such as the first vessel, 10, using the method of the invention.

[0098] Fig. 3 represents 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.

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

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

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

[0102] In the case of [Fig.3], the first vessel 10 has different stenosed portions STi, ST2 or non-stenosed 6 that can be selected by means of a selector or an automatic method of detecting variations in diameters. Image representation

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

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

[0105] Figure 2 illustrates the result of the first segmentation with the creation of the center lines for each arterial vessel. This step is implemented at the VIEW stage of Figure 1.

[0106] A first SEGi segmentation allows the images of the imaging system to be collected and the pixels of interest to be selected from a vessel or more generally from an organ.

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

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

[0109] According to one embodiment, a proximal reference point is defined with a parent artery. The distal reference point may correspond to a point in an area where an anatomical reference can be established, 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 angiography. However, if this limit were to decrease or if another, more powerful imaging system were used, the invention could be applied to a vessel up to a distal end having a radius of less than 1.5 mm in order to establish a new distal reference.

[0110] The first SEGi segmentation allows the outer surface of the vessel and the inner surface of the vessel to be delimited and a mean centerline of the vessel to be calculated.

[0111] According to one embodiment, the method of the invention comprises implementing a rectification algorithm to generate a display of the vessel in a 2D representation along an Ox axis which can define, for example, the centerline of the vessel

[0112] The first SEGi segmentation includes the ability to define a marker along the vessel on the 2D or 3D representation in order to visualize cross-sectional planes of the vessel. To this end, a selector allows a user to select a cross-sectional plane from a marker.

[0113] According to one embodiment, the first SEGi segmentation allows for the delimitation of portions of all or part of a vessel or artery in order to select and mark said portion for annotating the representation. One advantage is that it allows for the annotation of metadata portions that can be used during the training of the MLAI machine learning model or during the processing of the M0D2 CFD model, also known as CFD. Representation of the selected vessel

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

[0115] One advantage of this representation is that the diameter or inner radius of a portion of a vessel or artery containing 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 artery.

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

[0117] Preprocessing and extraction of anatomical features

[0118] Anatomical data are used to define part of the input data for the MLAI machine learning model and are also used for training the MLAH model

[0119] According to one embodiment, the input data of the trained model includes a first set of ENSi data characterizing the anatomy of at least one vessel from an acquired image of the individual. The method allows the selection of a first vessel 10 from an acquired image and the automatic extraction, through image processing, of data characterizing each portion 6, ST of the first vessel 10.

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

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

[0122] In one embodiment, the method includes a step of calculating the curvature of the vessel at different points of the vessel. In one embodiment, a function Cb(x) defines the function for determining the curvature as a function of of the position x on the longitudinal axis Ox of the representation of the straightened vessel in [Fig.4] or of the central axis of the non-straightened vessel.

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

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

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

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

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

[0128] According to one embodiment, all the curvatures of 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 image analysis, all the values ​​of the radii or internal diameters and all the curvature values ​​of the vessel 10 in question. These values ​​are stored in memory, and each value is associated with a position of vessel 10 along the longitudinal straightening axis. - Singularity

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

[0130] According to a first example, a first type of singularity is a plate 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 identified.

[0131] In the following description, the case where plaques 4 lead to the formation of one or more ST stenoses will be considered as an example. - Stenosis

[0132] Figure 4 illustrates an example in which two stenoses, ST1 and ST2, are identified through image processing. Automatic stenosis detection can be configured by automatically analyzing the variation in the internal diameters or radii of the vessel over the entire analyzed portion. Figure 4 shows plates 4 that do not contain stenoses and others that contribute to the formation of ST1 and ST2 stenoses. The method of the invention allows for the identification and annotation of the presence of stenoses on a vessel image.

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

[0134] The presence of an ST stenosis results from a local reduction in the radius or internal diameter of the first vessel 10. Each ST stenosis can be detected and identified using an image analysis algorithm. Various existing algorithms, such as the previously mentioned autoencoders, can be applied within the scope of the present invention. Stenosis detection allows for their enumeration along the first vessel 10. Vessel segments containing an ST stenosis are indexed, and the presence of said ST stenosis can be characterized by a set of xs positions along the Ox axis. The stenoses in [Fig. 4] are denoted ST1 and ST2.

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

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

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

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

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

[0140] According to one embodiment, the distance between two stenoses ST1 and ST2 can also be taken into account by a measurement on the image. The measurement can advantageously be performed automatically using an image processing algorithm. This data can be used for training and / or processing the trained MLah model.

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

[0142] The case in the following description is considered where a vessel is considered entirely from an entry point, usually an area of ​​junction with an artery and a distal end defined by a geometric or anatomical marker.

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

[0144] The pressure curve allows visualization of the pressure evolution along the vessel. This curve, although shown in [Fig. 4], cannot be obtained directly from imaging. The method of the invention overcomes this limitation. problem since the objective of the invention is to predict pressure values ​​along vessel 10 from a trained MLai machine learning model.

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

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

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

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

[0149] This representation illustrates the pressure drops after the presence of a stenosis.

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

[0151] The input to the MLAi machine learning model corresponds to the entire vessel or artery considered, as shown in [Fig. 4]. The artery or vessel is a topological unit, extending 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 extraction of anatomical features, the flow rate q, or the pressure p at the junction zones, allows the different junction constraints to be taken into account.

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

[0153] The anatomical data defined above define a part of the input data, denoted ENSb, of the MLAb machine learning model

[0154] According to one embodiment, the input data of the trained MLAl model include a second dataset ENS2 characterizing the individual. Input throughput

[0155] According to one embodiment, the resting inlet flow rate Qrest is calculated from the myocardial mass Mc, which is an input value of the system. An algebraic model allows the resting inlet flow rate Qrest to be expressed in terms of the myocardial mass Mc.

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

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

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

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

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

[0161] The first LAD artery refers to the artery called "Left Anterior Descending artery" in Anglo-Saxon terminology and in French: "L'artère interventrculaire antérieur". This artery supplies the anterior part of the heart, in particular the left ventricle.

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

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

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

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

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

[0167] Qrest = 2.5 * (Mc° 75) [ml / min],

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

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

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

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

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

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

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

[0175] If only the mass of the left ventricle is known, the relationship can be written Qhyp = Qrest_LV * khyp

[0176] In one embodiment, the model includes only the myocardial mass Mc as input. In another embodiment, the model includes both the myocardial mass and the resting cardiac output as input. It is understood that the two inputs Qrest and Mc are strongly correlated and therefore only one value can be considered as input to the MLAP model. However, the model can take both inputs into account. Patient data

[0177] These data are labeled ENS2 on [Fig.5] and ENS2' on [Fig.6] for the "in vivo" training data. According to one embodiment, the individual's heart rate is the input to the MLAi model.

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

[0179] In one embodiment, the individual's age is an input to the MLAi model. In another embodiment, the individual's gender is also an input to the MLAi model.

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

[0181] According to one embodiment, antecedent 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, and the quantification of tobacco use. Contextual data Standardization

[0182] The FFR estimation method of the invention includes 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 denoted NML in [Fig. 5] and [Fig. 6]. The normalization step NML is therefore designated as such in training or in operation of the machine learning model MLAH. The normalization steps are by design so as to generate normalized outputs regardless of the training data. Thus, only the input data may change upon input to the NML blocks.

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

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

[0185] According to another embodiment, the NML normalization step includes an upgrade of the accuracy and format of the data. NML normalization makes it possible to generate the data format that allows the input vector to be processed in the same way that the input vector was used for training in the different training branches.

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

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

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

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

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

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

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

[0193] Based on the pressures produced by the MLAb model, the process of the invention includes a step for calculating the FFR, namely the Pd / Pa ratio. This step is shown in [Fig. 5], illustrating the process for estimating the FFR or the outlet pressures. This step is also shown in [Fig. 6], representing the drive process.

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

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

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

[0197] According to an embodiment corresponding to that of [Fig. 7C], the values ​​of interest are the equilibrium pressure Po, the resistance R, the compliance C, and the impedance Zc at the outlet of the considered portion, i.e., calculated at the outlet cutting plane. In [Fig. 4], this outlet cutting plane is the plane pc6. In [Fig. 11], this cutting plane can be defined at point(s) OBi, OB2, OB3, or OB4. Model

[0198] The invention implements a model for predicting the pressure and other associated characteristics of a container, 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 the "PINN" network. Such a network is particularly well-suited for learning physical laws, especially nonlinear ones, for example, those approximated by differential equations. One advantage of such a network is its ability to work on physical processes in stenosed vessels. However, PINN can only provide solutions for defined vascular parameters, such as the vessel geometry or the position of the stenosis.The inclusion of each new parameter value requires a separate simulation, involving a complete recycling of the PINN. To overcome these limitations, one embodiment uses a physics-based DeepONet, also denoted "PIDeepONet". Such a network is referred to as the MLAI model in this application. The PIDeepONet can be used to learn various linear or nonlinear operators and impose physical constraints. DeepONet Network

[0199] According to one embodiment, the method of the invention implements a machine learning algorithm (MLAi) 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 a "mapping" in Anglo-Saxon terminology. It transforms one function into another. The DeepONet network learns this transformation directly from ENSf training data.

[0200] In a DON-type 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', ENSI”, ENSi'”.

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

[0202] In order to represent the mathematical operator from the data, the DON network allows us to consider two components generally denoted "trunk" and "branch" in Anglo-Saxon terminology. The "trunk" component or branch is denoted Bt and the "branch" component or branch is denoted Bb in the remainder of the description.

[0203] Figure 7A represents an architecture of a network called in Anglo-Saxon terminology "Physics-informed DeepONet". This example of a DON-type architecture is advantageously implemented in the process of the invention.

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

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

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

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

[0208] Figure 7C represents an example of an n-outlet architecture used within the framework of the invention to generate different outputs, here represented by the pressure P, the flow rate Q, the cross-sectional area A, and the cross-sectional area Ao at equilibrium. In this figure, the outputs Secondary outputs are shown. These secondary outputs are data calculated subsequently from the data produced by the MLAh network. They are therefore obtained indirectly. Figure 7C shows, in particular, the FFR obtained along the vessel axis, the equilibrium pressure Po, the impedance Zc, the compliance C, and the resistance R.

[0209] The model can be expressed as a function G(u)(y) taking as inputs of the model the two inputs {u(xi)]i and {yk}k to generate a prediction. Pi \ ' < ■ ■ \ Gg} I (w(xil«hz),...,My) + &&? 1 fcspj-i+l \ Vranc'i transe ' [Math 1]

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

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

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

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

[0214] u(Xi) is a function that returns the parameters used to describe the different anatomies of vessels or portions of vessels defining the anatomical training input data ENSi'. u(xi) is a function that processes the ENS / training data in order to train the MLAi model.

[0215] u(Xi) corresponds to the input functions, which describe the geometric / anatomical characteristics of the vessel at 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 signifies the absence of stenosis. In another embodiment, the functions u(x) are determined by an internal representation generated by the autoencoder network. In this case, the construction of u(x) is an unsupervised learning process. The Bb branch of the DON processes the operator input. This input is generally a function or a set of values ​​that represent a function.

[0216] The Bb branch 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 certain characteristics of this function.

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

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

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

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

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

[0222] According to one implementation example, the DON network comprises only one branch, Bb. Such a network is called an "unstacked DeepONet" in Anglo-Saxon terminology. It has the advantage of being less computationally intensive in matrix operations.

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

[0224] According to one embodiment, the DON network takes physical constraints into account. In Anglo-Saxon terminology, the network is called a "physics-informed DeepONet." Such a network allows physical constraints to be taken into account in the configuration of the loss function, thereby penalizing predicted values ​​outside a predefined range. Loss functions

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

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

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

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

[0229] With, according to an example, the following expression of the two operators: sp ($) - VF / ZR [Math 2] Q in m=^ZZZ k■ i=l J=1 fc=l [Math 3]

[0230] Where {yk(i)}k =i ùq denotes a set of points randomly sampled in the domain G(u(i)).

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

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

[0233] This system of equations takes the form of a numerical model of hemodynamic equations called MODi. It can be expressed as follows: 1 dq 1 d —F + — ^7=°' dx dt 1 dq 1 d A?2\ 1  dp 4 q has x ^dx\ÂJ ^ X ,pdx [Math 4]

[0234] 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 equations [4]. These hemodynamic equations can be modeled in 1D, 2D or 3D.

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

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

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

[0238] The parameters and variables are defined as follows: q = ----U = -----, p = ----, Ao = ----■ Hmax ^max Pmax ^max jnmax NK . i „ i y 7T [Math 5]

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

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

[0241] Furthermore, the method of the invention allows for the consideration of another target variable. For the additional variables q, p, A, Âq-, additional constraints have been defined, namely: Cq, Cp, C^, C^Q.

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

[0243] [0 ; 1]

[0244] C^ = [0;l]

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

[0246] C£n= [7e-06, 1]

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

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

[0249] Figure 6 represents the MLAi model during its different training phases, labeled Bb, B2, and B3, providing three inputs to the network for training. These three inputs are represented in Figure 6 by blocks Bb, B2, and B3, allowing for a better understanding of these different training phases. The test and validation data for each of these branches, E2, E3, and E4, are represented as outputs of the three data normalization blocks, labeled NML.

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

[0251] Indeed, the first input aims to train the MLAi model with data tested in vivo, that is, with patients for whom pressure measurements are taken via a catheter. The second input aims to train the MLAi model with a CFD solver capable of solving a system of incompressible Navier-Stokes differential equations. The third branch aims to train the MLAi model with data measured on a test bench; these measurements are referred to as in vitro measurements.

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

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

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

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

[0256] A second input labeled “cfd” in [Fig.6] allows the machine learning model MLAI to be trained. According to one embodiment, a training dataset corresponding to the E3 test and validation data is obtained by solving a so-called “1D CFD” model.

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

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

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

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

[0261] To this end, the training method of the invention makes it possible to automatically generate cross-sectional planes of the vessel in order to consider each segment as a portion of the vessel whose blood flow properties can be calculated using the MOD2 hemodynamic model. One benefit is to calculate test values ​​to train the machine learning model.

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

[0263] Fig. 4 also represents different cross-sectional planes generated in particular during of the second segmentation SEG2. These section planes are labeled pcB pc2, pc3, pc4 pc5, pc6 on [Fig.4]. They are generated to delimit the different types of portions in the second segmentation.

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

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

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

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

[0268] According to one embodiment, when using the M0D2 hemodynamic model, also known as CFD, each segment considered corresponds to a physical type of the portion of the vessel under consideration, namely a non-stenosed portion, a stenosed portion, a curved portion, and a portion containing a bifurcation. According to this embodiment, this rule makes it possible to define that two adjacent segments are always of different types.

[0269] Fig. 11 represents an example of a second segmentation SEG2 used to generate training data from a model of eigenhemodynamic equations M0D2. In this model, different equations can be applied to different types of portions having a model of eigenhemodynamic equations.

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

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

[0272] A first type of segment sgb sg3, sg4, sg6, sg8, sg9, sg10, sgn, sg13, sg14, sg16, sg17, sgi9, sg2i, corresponds to the portions of vessel in which the flow can be modeled by equations of the CFD solver, called 1D Navier Stokes equations denoted [1] and [2], allowing the flow to be modeled and the pressures to be calculated within the vessel(s) by considering initial assumptions on the flow.

[0273] According to one embodiment, the method of the invention is carried out for each branch from the entry point IBi to the various exit points OBh 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 cross-sectional area A(x, t), that is to say at every point along each vessel and at every instant of the cardiac cycle.

[0274] 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.

[0275] A second type of segment, sg5, sg7, sg[2j sg20], corresponds to portions of the vessel exhibiting stenosis, that is, a local reduction in the vessel diameter exceeding a certain threshold. Portions with stenosis necessitate the use of a dedicated flow model, different from the model used for circulation in a non-stenosed portion. In this case, an equation

[21] described below can be used to model the blood flow and calculate the inlet and outlet pressures of each stenosed portion, taking into account initial assumptions about the flow.

[0276] A third type of segment, sg2, sg8, corresponds to portions of a vessel with a curvature exceeding a certain threshold and which can affect the flow pattern compared to flow in a non-curved portion. In this case, an additional equation can be used to model the blood flow by considering initial assumptions about the flow pattern.

[0277] A fourth type of sgi5 segment corresponds to vessel portions exhibiting an aneurysm, i.e., portions with a local bulge in vessel diameter exceeding a threshold. A local bulge can be detected due to a local increase in the vessel's internal and / or external diameter exceeding a threshold. The threshold can be expressed as an absolute value or as a proportion of the mean vessel diameter or the diameter in an adjacent portion. The threshold can also be characterized by the local variation in diameter. Portions with a local bulge can be better modeled by [the modeling method] [which requires the use of a dedicated model of] circulation flow differs from the model used for circulation in a portion of the first type, for example. In this case, a semi-empirical equation similar to equation

[21] described below can be used to model blood flow, considering initial assumptions.

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

[0279] In order to delimit the cutting planes during this second segmentation SEG2, the training method of the invention makes it possible to detect variations in the diameters or radii of the first vessel. Thus, after a reduction in diameter exceeding 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. Similarly, after an increase in diameter exceeding 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. Continuity conditions at the boundaries of segmented portions#

[0280] The second segmentation SEG2 allows for the definition of a continuity condition between two successive segmented portions, particularly with regard to the values ​​estimated by the different M0D2 models applied according to the type of segment. Specifically, 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. Conversely, the pressure or flow rate at the inlet of a second portion is equal to the pressure or flow rate at the outlet of a first portion directly preceding the second portion. This is also true for other parameters characterizing the flow or the boundary conditions at the junctions between segments.

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

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

[0283] With regard to the stenotic portions, a mathematical method for managing the boundary conditions can be implemented. For example, a method known as "ghost cells" can be implemented. These ghost cells are added to the mesh cells.

[0284] According to one embodiment, the feedback loop makes it possible to test which type of segment is being 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 phantom cell.

[0285] The principle is to define a physical grid of space allowing calculations to be performed, where each cell represents a volume of fluid. The phantom cells allow boundary conditions to be defined for pressure, flow rate, etc., within the phantom 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 various types, such as Dirichet conditions for fixed values, Neumann conditions for gradient-type values, or more complex conditions like sliding or periodicity conditions. For example, the condition on the time variable t can be derived from the constraint of the heart rate. The integration of the Navier-Stokes conservation equations is performed on each cell and also on the phantom cells.

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

[17] at the output, i.e. in the case of [Fig.11], at the points OBi, OB2, OB3 or OB4, allow the equations to be solved step by step.

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

[0288] The various geometry segmentations created in vitro can be used as many different case studies for M0D2 CFD modeling. One advantage is the ability to generate a large amount of training data to cover many different configurations. For example, cases in which several stenosed segments occur consecutively within the same vessel.

[0289] Furthermore, this geometry data from the 3rd segmentation SEG3 allows for the validation of CFD models. Thus, the choice of equations, particularly equation

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

[21] can be adjusted according to The different geometries of stenotic portions or other coefficients can be calculated and fitted for other semi-empirical equations.

[0290] In another case, the data are obtained from vessel data already stored in memory. The data source is labeled PRODi in [Fig. 6]. The geometric data are labeled Ei. In one example, the geometric data come from the same images as the in-vivo data of entry Bi in [Fig. 6]. One advantage is that it allows comparison of CFD predictions with in-vivo measured data.

[0291] The 1D CFD model is obtained by applying the Navier-Stokes equations to each segmented portion or group of portions of the first vessel 10. [Sq ' gq=()4Math6] dx dt [Math 7] | ri + A dp _ 4 ÔZ dx\A / p dx ÔRe

[0292] Where: [Math 8] Â = A / A mox [Math 9] 2qfIMT, [Math 10] A e =—=—; vv jr X ..

[0293] We consider x a coordinate along the Ox axis of straightening of the vessel, t is the time parameter, p is the pressure, q is the flow rate, A is the section, ô is the thickness of the boundary of the wall of the layer and v is viscosity.

[0294] Equations (1) and (2) can be derived with an assumption of uniform pressure within a section of the vessel.

[0295] The velocity profile is denoted here as u and can be expressed as follows: I / / r A> ï Mathll l = ? [ « ( J? — f ) / Ô, R — Ô < R

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

[0297] According to one embodiment, a state equation that associates the pressure and the cross-sectional area of ​​the vessel can also be added to the system of equations: / —[Math 12]

[0298] Where!------ , [Math 13] Eh '[Math 14] Eh=---- J Pma. V jy

[0299] With the following definitions of the constants or parameters taken into consideration: 2, [Math 15] JT f'fi [ p... »

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

[0301] E is the Young's modulus.

[0302] h is the thickness of the vessel.

[0303] According to one embodiment, the experimental data give the following relationship which links these parameters: Eh_. , [Math 16] ---— “ + / 0, Z q

[0304] Where

[0305] ki = 2«107 g / (s2«cm)

[0306] k2 = 22.53 cm-1

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

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

[0309] According to one embodiment, the wall thickness 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 vessel thickness can be modified according to parameters such as individual profile parameters: like age or gender, and parameters extracted from imaging. In one embodiment, the thickness of the vessel under consideration is taken into account in the vessel elasticity model.

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

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

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

[0312] According to one embodiment, among the values ​​used for the boundary conditions, we find the resistance Ri or the characteristic impedance Zc, the resistance R2 and C compliance.

[0313] The output conditions can be obtained from the Windkessel equation. The latter is written as a function of the pressure parameters p and flow rate q: , [Math 17]

[0314] Where: ' AJ?= 77 HAS C —--77— , [Math 18]

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

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

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

[0317] According to one embodiment, values ​​of constants Ri or Zc, R2, and C can be estimated from in-vitro data using the pressure wave velocity, denoted PWV and known in Anglo-Saxon terminology as "pressure wave velocity". It is calculated using two distant pressure sensors, considering a known distance.

[0318] The impedance Ri and the compliance C can be obtained, for example, from the following equations: / ? : jz p * PWV / A [Math 19] A, [Math 20] "777WW

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

[0320] However, these methods do not allow for adjusting and adapting the values ​​to each individual.

[0321] Thus, training the machine learning model allows the learning function to be learned from the in-vivo measured data and the CFD model.

[0322] The invention allows, in a second step, when the machine learning model has been trained, to deduce these values ​​from the application of the MLAi machine learning model with operating data from the ENSi dataset.

[0323] Equations [6] to

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

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

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

[0325] 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: A>i s 2 K V ^Â< kJÂ.. ----_^ = ---- + —L —2 2 \2, [Math 21] /

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

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

[0328] In this example, the cross-section is assumed to be constant along the entire length of the stenosis. It should be noted here that the notations are similar to those of the output of the MLAI model, denoted Si; however, they do not represent the same variables or parameters.

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

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

[0331] Equation

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

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

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

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

[0335] A method for estimating these coefficients can be based on the implementation of a machine learning model that allows the coefficients to be learned from a plurality of measurements whose values ​​characterizing the fluid flow are known due to the test bench.

[0336] Equations [6] to

[15] can be solved numerically, for example, using the MacCormack method, considering a given system order and boundary conditions. The 1D CFD model can be applied to cases of varying complexity, from a simple unobstructed vessel to a network of branching vessels exhibiting 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 preprocessing software identifies and divides the complete geometry into a set of "segments" and creates a topological diagram describing their interconnection, as shown in [Fig. 11].

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

[0338] If the modeled vessel system(s) 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 [Fig. 11] at the junction points ABi, AB2, AB3.

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

[21] .

[0340] Appropriate equations such as equation

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

[15] for example, various elasticity treatments

[12] and

[15] , velocity profile

[11] or boundary conditions

[17] .

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

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

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

[0344] A third input B3, labeled "In vitro" in [Fig. 6], allows the machine learning model MLAI to be trained. According to this method, a test bench 20 is defined to control a flow geometry and measurements at various 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. To train the model, measurements can be taken in various ways. One method aims to model sections of pipes and measure the fluidic and mechanical properties of the flow within these sections, for example, by measuring pressure from a pressure sensor, flow rate from a sensor or Doppler ultrasound, viscosity from a viscometer, and elasticity, for example, from a tensile test.

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

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

[0347] An example of a test bench 20 modeling fluid flow within different portions is shown in [Fig. 8]. Such a representation is illustrated by way of example; other examples of test benches can be made within the scope of the present invention. One advantage of this test bench is that it allows for the representation of any type of segmentation. This test bench 20 can correspond to a third segmentation SEG3, which may, for example, mimic or not specific cases of vessels in vivo.

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

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

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

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

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

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

[0353] Narrowing profiles are noted such as the P profile defining a narrowing along straight lines. An S20 profile defines a narrowing along curved lines. A Si profile defines a narrowing along curved lines with An asymmetry in the variation of the narrowing is observed between the downstream and upstream portions of the stenosis. Profile S30 exhibits the opposite asymmetry to profile S10. Profile PU shows a narrowing with straight lines exhibiting asymmetry within the cross-section. Profile SU shows an asymmetrical variation in diameter within the stenosed portion between the upper and lower parts of the vessel. Profile PU2 also exhibits asymmetry and an induced flow orientation along an axis that is not collinear with that of the vessel. It is possible to use two profiles from [Fig. 10] to simulate a scenario in which two or more stenoses are present, as in the case of [Fig. 4].

[0354] The geometric data thus modeled allows for the production of numerous scenarios. The source of this data is labeled PROD2 in [Fig. 6]. The PROD2 source corresponds to the production of the input anatomical descriptors used to define the input data ENSi'” of the MLAP model

[0355] As in the context of CFD, the PROD2 component allows the geometric data and the data of all in-vitro measurements Q, P, A to be produced from the sensors arranged on the test bench 20.

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

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

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

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

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

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

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

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

[0364] The multi-fidelity method approach is particularly advantageous in applications of uncertainty optimization and quantification, as 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 levels of fidelity. Entry B1: Training with in vivo measurements

[0365] A first input, Bi and labeled "In-vivo" in [Fig. 6], allows the machine learning model MLAi to be trained using data from patients. The notation "In vivo" does not necessarily refer to manipulations performed on a living being, but rather to the fact that the data come from living beings, more specifically from humans. The ENS2' patient data used are stored in memory prior to their use.

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

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

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

[0369] 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.

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

[0371] The training data, for the in vivo case, includes in this case the E2 test data shown in [Fig.6]. According to one embodiment, the training data includes on the one hand the ENSf data extracted from the anatomical descriptors and the ENS2' data, referred to as patient data, as well as the measured E2 data allowing validation of the predictions made by the MLAi model.

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

[0373] List of equations [Math n]

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

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

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

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

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

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

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

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

[0382] [9]: equation allowing normalization of estimated values, particularly of time and of pressure and in particular in equations

[61] and

[72] ;

[0383]

[10] : expression of the Reynolds number;

[0384]

[11] : equation describing the velocity profile;

[0385]

[12] : equation of state of pressure;

[0386]

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

[0387]

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

[0388]

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

[0389]

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

[0390]

[17] : Windkessel equation;

[0391]

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

[17] ;

[0392]

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

[0393]

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

[0394]

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

Claims

Demands

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

2. Method according to claim 1 characterized in that the extraction of the first data set (ENSi) is obtained by means of 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 a first vessel (10) displayed on a display, the selection of a point of the vessel.

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

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

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

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

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

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

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

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

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

12. A method according to any one of the preceding claims characterized in that it comprises a training step (B3) carried out from a third set of 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 (MLAi) being supervised so that the values ​​characterizing the flow of a fluid in each portion are measured on a test bench (20) comprising at least one test pipe portion and sensors enabling the measurement of test data (E4) at different points of said test bench (20) comprising in particular the flow rate, pressure, viscosity, fluid resistance, Reynolds number and fluid density.

13. Method according to claim 12 characterized in that it comprises a characterization of the different portions of the test bench (20), each portion being characterized by 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.

14. Method according to claim 13 characterized in that it comprises an injection of a fluid within the test bench (20) reproducing a periodic activity related 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.

15. A method according to any one of claims 13 to 14 characterized in that the third training data set (ENSi'”) also includes a measurement and calculation for at least one point of each predefined pipe portion: • of at least one output resistance (R, R2) modeling the force opposing the flow of blood in the portion of the first vessel (10); • of at least one impedance (Zc, RJ); • of at least one fluid viscosity value; • of at least one equilibrium pressure value (Po).

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

17. The method according to claim 16, characterized in that a second segmentation (SEG2) of the first vessel (10) generates automatically a plurality of segment types (6, STb ST2) including: • a first segment type (6) defining substantially regular portions corresponding to portions of vessels having a cross-section decreasing progressively from a proximal end to a distal end; • a second segment type (ST, STB ST2, sg5, sg7, sgi2, sg20) defining at least one irregular portion, said at least one irregular portion corresponding to a portion having at least one narrowing of the diameter greater than a predefined threshold, each of the sets of segments having a system of equations modeling the hemodynamic flow in said portion.

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

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

20. A method according to claim 19 characterized in that the system of equations comprises a second hemodynamic numerical model (MOD2) comprising for each portion of vessel at least one model among which: • A mass conservation model and / or; • A momentum conservation model and / or; • A pressure state equation and / or; • A first pressure delta model and / or; • A second pressure delta model established from in-vitro measurements.

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

22. A method according to any one of claims 16 to 21 characterized in that the second numerical hemodynamic model (M0D2) allows for the estimation, for each portion of vessel of the second type (ST, SU, ST2), of a pressure delta from a pressure delta model comprising a viscous resistance coefficient (kv) and a turbulent resistance coefficient (kT).

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

24. A method according to any one of claims 16 to 21 characterized in that the first machine learning model (MLAi) is trained by considering the values ​​estimated by the second model (M0D2) integrated over the whole of the first vessel (10).

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

26. A method for training a machine learning algorithm to produce a trained network (MLAi) capable of 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 one 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 of a first numerical model of hemodynamic equations (MODO, said training method comprising: • Acquisition of an initial training dataset (ENS / , E2) from: • Acquisition (ACQi) of a first image (IMi) of an imaging system; • Extraction (EXTi) of a first training dataset (ENS / ) defining anatomical descriptors of a first vessel (10) of said first image (IMi); • Acquisition of a patient data set (ENS2'), including at least heart rate (HR) and myocardial mass (Mc); • Reading data (E2) characterizing pressure measurement points of a first vessel (10) defining test and validation data of a machine learning model (MLAJ; • Execution of the machine learning model (MLAi) whose inputs include the first set of training data (ENS1') and data generated from patient data (ENS2') and learning by implementing a cost function minimizing the error between a data produced (S2) by the model (MLAi) and the test and validation data (E2); • Acquisition of a second training dataset (ENS / ', E3) from: • Acquisition (ACQi) of a first image (IM / of an imaging system; • Extraction (EXT / of a second training dataset (ENS / ') defining anatomical descriptors of a first vessel (10) of said first image (IMJ; • Solving a solver (CFDi) modeling a (M0D2) model of hemodynamic equations from the incompressible Navier-Stokes equations in one dimension, the estimated data (E3) by the solver (CFDi) defining test and validation data for a machine learning model (MLAi); Execution of the machine learning model (MLAi) whose inputs include the second training dataset (ENSi”) and learning by implementing a cost function minimizing the error between a data produced (S3) by the model (MLAi) and the test and validation data (E3); Acquisition of a third training dataset (ENSi'”, E4) from: • Modeling of a set of geometries defining pipes adapted to convey a fluid whose viscosity is approximately that of blood and adapted to be arranged within a test bench (20); • Execution of a set of fluid flow tests with a variety of different geometries within the test bench (20); • Data measurement (E4) characterizing pressure measurement points of a first channel portion defining test and validation data of a machine learning model (MLAi); Execution of the machine learning model (MLAi) whose inputs include the third training dataset (ENSi) and learning by implementing a cost function minimizing the error between a data produced (S4) by the model (MLAi) and the test and validation data (E4).

27. Method according to claim 26 characterized in that the first machine learning model (MLAi) is a DeepONet network.

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