FR3115108A1 - Determination of a quantity characterizing a medium by constrained tomography - Google Patents

Abstract

Determination of a quantity characterizing a medium by constrained tomography Method for characterizing a medium, using an inversion algorithm, at least one tomographic image of said medium acquired beforehand and at least one datum, called stress, representative of at least a standard quantity of said medium or medium(s) similar to said medium, method in which said inversion algorithm is used to extract at least one piece of information from said at least one tomographic image, and at least one characteristic quantity of at least one property of said medium is determined from said at least one item of information extracted and by using said inversion algorithm of which at least one parameter is modified as a function of said at least one constraint datum. Figure for abstract: Fig. 1

Description

Determination of a quantity characterizing a medium by constrained tomography

The present invention relates to methods and systems for the characterization of a medium under test.

Tomography is a microwave imaging technique used in many fields including medical imaging, geophysics and mechanics of materials. This technique makes it possible to reconstruct the volume of an object from a series of measurements taken from the outside of this object, in particular using sensors, and reconstructing certain properties of the interior of the object.

In a known manner, tomographs are composed of radiating elements used to illuminate the domain under test and of one or more receiving elements capable of capturing the field diffused by the domain under test. Since microwaves can penetrate inside dielectric materials, information regarding the internal structure of the tested object can be retrieved from the measured scattered field data.

The radiating elements can be antennas and the scattered field can be picked up by these antennas controlled by a computer-controlled switching board connected to a vector network analyzer (VNA).

The acquired data is then processed with an inversion or reconstruction algorithm whose final goal is to recover a spatial map of the dielectric properties of the interior of the object, such as the dielectric permittivity or the electrical conductivity.

There are different inversion algorithms that can be classified into two categories:

• analytical algorithms, based on a continuous representation of the problem by mathematical formula, for example the Radon transform. Often simple and quick, they generally do not take into account the statistical nature of the measurement; And
• algebraic algorithms, based on a discrete, often matrix, representation of the problem. Rather more elaborate, they allow the use of a direct model obtained by numerical simulation and use statistical modeling of the measurement to reverse the problem using probabilistic methods, based on criteria such as maximum likelihood or maximum a a posteriori and according to iterative methods such as the expectation-maximization algorithm.

Examples of tomographs and inversion algorithms are described in the articles IEEE 2018 "Design and Experimental Test of a Microwave System for Quantitative Biomedical Imaging" , Springer 2017 "A numerical study concerning brain stroke detection by microwave imaging systems" and Journal of Imaging 2018 “A Tomograph Prototype for Quantitative Microwave Imaging: Preliminary Experimental Results ”.

In recent years there has been a growing interest in the use of tomographs in biomedical applications, both for therapy and for diagnosis.

In particular, for the monitoring of delicate target parameters such as blood sugar, the tomographic approach has the advantage of being a non-invasive solution, which is an interesting alternative to invasive solutions which can be restrictive and painful, and involve a risk. significant infections and allergies.

However, the image obtained by conventional tomography is not sufficient to obtain precise information on the target parameter allowing the characterization of the medium under test.

There is a need to further improve the methods for characterizing a medium using a tomographic technique, in particular with a view to accurately characterizing a characteristic quantity of the medium under test.

The invention aims to meet this objective and it achieves this, according to one of its aspects, thanks to a method for characterizing a medium, using an inversion algorithm, at least one tomographic image of said medium previously acquired and at least one datum, called constraint, representative of at least one standard quantity of said medium or medium(s) similar to said medium,

method in which said inversion algorithm is used to extract at least one piece of information from said at least one tomographic image, and

at least one characteristic quantity of at least one property of said medium is determined from said at least one item of information extracted and by using said inversion algorithm of which at least one parameter is modified as a function of said at least one constraint datum.

Said at least one parameter of the inversion algorithm can be replaced by said at least one constraint datum.

The inversion algorithm is thus advantageously constrained by the constraint data or data to converge towards the determination of the desired characteristic quantity.

The characteristic quantity can be an electromagnetic quantity, such as the dielectric permittivity or the magnetic permeability, or a physiological parameter such as blood sugar.

The constraint data, also called “ a priori data ”, are the quantities characterizing the medium under standard conditions, serving to direct the algorithm towards the determination of the characteristic quantity, and whose values are lower than predetermined thresholds.

In the case of glycaemia, it is possible to include pathological blood glucose content thresholds, and thus provide a variation of this data. For a healthy subject, the threshold may be 1 g/litre. The threshold of 0.8 g/litre characterizes hypoglycemia, and 1.2 g/litre corresponds to hyperglycemia. The variations of the dielectric quantity are of the order of 1 to 10%, offering a fine measurement.

Thanks to the invention, the algorithm used is reinforced by the so-called constraint data, thus making it possible to supply a scalable database and to increase the speed of convergence of the calculations, increasing the precision of determination of the said characteristic quantity.

Preferably, several previously acquired images are used to form an information sequence also comprising the stress data or data, in particular by concatenation, said information sequence being used for determining said at least one characteristic quantity, the sequence of information being obtained in particular by “ deep learning ” . The information sequences obtained can be recorded in a database as acquisitions are made, said database being used in the implementation of the method according to the invention.

Inversion algorithm

Any inversion algorithm of the gradient algorithm or Gauss-Newton algorithm type can be used to implement the method according to the invention. Examples are given in the publications Elsevier 2019 “Microwave tomographic imaging of cerebrovascular accidents by using high-performance computing” and IEEE 2018 “Examination of the Sensitivity Matrix During the Iterative Reconstruction Process for Microwave Tomography” . Another example of an inversion algorithm is the one described in the IEEE 2018 publication "Design and Experimental Test of a Microwave System for Quantitative Biomedical Imaging" , in section III. An example of a constraint that can be applied to this algorithm is to give extreme values to the permittivity. In other words, it is possible to constrain the permittivity to vary only within a well-defined interval, as a function of the target characteristic quantity. Furthermore, the basic principle of the inversion algorithm described in the IEEE 2020 article “An Algorithm to Image Individual Phase Fractions of Multiphase Flows Using Electrical Capacitance Tomography ” is the minimization of a conventional cost function.

Stress quantities and data

The standard quantity(s) of the medium may be maps or images of said medium or of medium(s) similar to said medium, or experimental values associated with said at least one property of the medium or of medium(s) similar( s).

The property of the medium can be a physico-chemical quantity chosen from concentration, temperature, pressure, viscosity, flow velocity of a liquid passing through the medium.

The information or information from the tomographic images may be quantities characterizing the medium under test, at the time of acquisition of the image.

In a preferred embodiment, the characteristic quantity is a physiological parameter, in particular blood sugar. In this case, at least one item of information from the image of the section of an arm and the stress data representative of dielectric quantities of healthy tissue(s) can be used to determine a blood sugar value, the inversion algorithm being constrained by the constraint data or data to converge towards the measurement of said blood glucose level. This makes it possible to detect variations in blood sugar and to accurately diagnose hypoglycemia or hyperglycemia.

The characteristic quantity may be the level of lactate in the blood. Microwave sensors for non-invasive measurement of blood lactate levels are described in IEEE publication 201 7 “ Non-Invasive Measurement of Blood Lactate in Humans using Microwave Sensors ”

As lactate is produced during intense muscular effort when the oxygen supply to the muscle tissues becomes insufficient, tissue hypoxia conditions can result.

In this case, at least one piece of information from the image of the section of an arm and the stress data representative of dielectric quantities of healthy tissue(s) can be used to determine a lactate value, the inversion algorithm being constrained by the at least one constraint data to converge towards the measurement of said blood lactate level. This makes it possible to detect variations in lactate and to accurately diagnose possible tissue hypoxia.

In another preferred embodiment, the characteristic quantity is the rate of a polluting product in an extraction medium, in particular a liquid, an object or a soil. In this case, said at least one constraint datum is a dielectric quantity or the value of a property of the extraction medium or of similar medium(s), such as the temperature, the pressure, or the speed of the flow. This makes it possible to detect variations potentially linked to the presence of the polluting product in the liquid, in order to diagnose a mixture of biofuels.

The polluting product can be water and the extraction medium a hydrocarbon, in particular in a pipe.

System

Another subject of the invention, according to another of its aspects, is a system for characterizing a medium under test, for the implementation of the method according to the invention, the system comprising:

• a network of tomographic sensors connected to the medium under test,
• a switch box connected to the sensors, and
• a processing unit comprising an integrated circuit configured to execute an inversion algorithm, to extract at least one piece of information from said at least one tomographic image by means of said inversion algorithm, and to determine a characteristic quantity of at least one property of said medium from said at least one item of information extracted and using said inversion algorithm of which at least one parameter is modified as a function of at least one datum, called constraint, representative of at least one standard quantity of said medium or medium(s) similar to said medium.

The sensor system according to the invention is completely non-invasive, simple to use and provides more precise and reliable target data.

The integrated circuit is preferably configured to execute an inversion algorithm, the constraint data(s) being used as parameters of said inversion algorithm for the processing of said information(s).

Preferably, the sensors are electromagnetic transducers, in particular very near field antennas.

The transducers may include at least one transmitter and at least one receiver.

For example, if N is the total number of transducers, n of them are dedicated to transmit, with 0 < n < N and (n-1) are dedicated to receive.

The N transducers can operate on transmission and/or on reception. When one of them is chosen for transmission, the other (N-1) are in receiver mode. Then, a second is chosen for transmission and the rest are receivers, and so on according to a circular permutation of the role of the N transducers.

Preferably, the switch box comprises switches ensuring that the same transducer can be sometimes transmitter sometimes receiver.

The processing unit is preferably configured to create an information sequence formed by the images coming from the network of sensors and the stress data or data, said information sequence being used for determining said characteristic quantity of at least a property of the medium.

Preferably, the array of sensors is attached to a peripheral support around a part of the body, in particular an armband around the arm, a bracelet around the wrist or a belt around the abdomen, which the user wears to monitor the variations in a physiological parameter of his body, in particular blood sugar.

This armband has the advantage of being comfortable to wear and does not require any invasion of the body.

In the case of determining the rate of a polluting product in an extraction medium, in particular in a fluid inside a pipe, the network of sensors is positioned on the internal or external periphery of the pipe.

The processing unit can be configured to use so-called learning or “ deep learning ” algorithms, in particular by means of neural network(s), in particular convolutional, and/or classifiers, in particular of the separator type wide-margin (SVM), Softamx type or RBF with Gaussian kernel.

Program product computer

Another subject of the invention, according to another of its aspects, is a computer program product for implementing the method according to the invention, for characterizing a medium, using an inversion algorithm, at least one tomographic image of said medium previously acquired and at least one datum, called stress, representative of at least one standard quantity of said medium or of medium(s) similar to said medium,

the computer program product comprising a medium and recorded on this medium processor-readable instructions so that, when executed, said inversion algorithm is used to extract at least one piece of information from said at least one tomographic image, and at least at least one characteristic quantity of at least one property of said medium is determined from said at least one item of information extracted and by using said inversion algorithm of which at least one parameter is modified as a function of said at least one constraint datum.

The invention may be better understood on reading the detailed description which follows, non-limiting examples of its implementation, and on examining the appended drawing, in which:

there is a block diagram illustrating the principle of the method according to the invention,

there schematically represents an example of a system for characterizing a medium under test according to the invention,

there schematically illustrates a side perspective view of a homogeneous medium under test,

there represents a top view of the medium under test of the ,

there schematically illustrates a side perspective view of an inhomogeneous medium under test, and

there represents a top view of the medium under test of the .

detailed description

There illustrates a block diagram explaining the principle of the method according to the invention.

A stress inversion algorithm, used in the tomography method of the medium under test, receives as input stress data modifying the parameters of said algorithm, as well as a previously acquired tomographic image of said medium.

This image can be acquired either by the same inversion algorithm used conventionally without any constraint, or by another inversion algorithm. The image and the constraint data constitute two constraints directing the inversion algorithm towards the determination of a target characteristic quantity.

Example 1

Schematically represented in an example of a system for characterizing a medium under test according to the invention for determining blood sugar.

The system 1 comprises an armband 3 that the user wears around the arm 4, a switch box 5 and a processing unit 7.
Armband 3 comprises a network of tomographic sensors 2 to produce the tomographic image of the section of arm 4.

In this example, the sensors 2 are electromagnetic transducers, such as very near field antennas.

These transducers can be transmitters and/or receivers. The switching box 5 to which the sensors 2 are connected comprises switches ensuring that the same transducer can be sometimes transmitter sometimes receiver.

In addition, the phases of each power supply of each transducer can be adapted.

Such a transducer may include a dipole antenna consisting of two sheets of metal separated by a feed space.

The processing unit 7 is configured to create an information sequence formed by the images originating from the network of sensors 2, and constraint data which can be recorded in a memory, not shown in the figure, connected to the unit treatment. The information sequence is then used to modify the parameters of the inversion algorithm for blood glucose determination.

The processing unit 7 is preferably connected to a computer 9 having a screen 8 where the results of the calculations can be displayed, in particular in the form of graph(s).

For the tomographic sensor system to operate in a real environment, around the arm of a patient in the example considered, it must be equipped with an integrated circuit, not shown, for the generation and management of the signal in transmission and in reception. This circuit is advantageously designed in a simplified manner around an architecture similar to that of a miniaturized and autonomous vector network analyzer.

Example 2

Figures 3a and 3b schematically illustrate a homogeneous medium under test, modeled by a circular cylinder of revolution, which can be deformed according to the application scenarios, and provided with six antennas on its periphery. The zone under test 20 inside the cylinder is homogeneous, that is to say that it consists of a single material. This material can be simple or in the form of a mixture of miscible materials (for example water mixed with certain alcohols such as ethanol) or inhomogeneous (for example oil and water).

The signals used are electromagnetic signals with frequencies between a few MHz and a few GHz.

In this example, the target values to be determined are variations of electromagnetic quantities of the area under test. Stress data are the properties of the initial materials or fluid displacement velocities. An example of target variation of interest is the appearance in the homogeneous test area of a concentration variation of the initial mixture or the appearance of an external material, such as a pollutant, in the initial material.

Example 3

Figures 4a and 4b, similar to Figures 3a and 3b, represent a heterogeneous medium under test, in which the area under test inside the cylinder comprises different materials. This is modeled by two different cylinders located inside the initial cylinder so as to have three distinct zones 21, 22, 23, with consequently three different values of dielectric quantities.

An image or images of the area under test are acquired and known standard values of electromagnetic quantities of materials are combined with the acquired images to constrain the inversion algorithm. The target value(s) to be determined are, in this example, the values of the electromagnetic quantities that vary over time.

In the initial state, all the materials of the three zones 21, 22, 23 have initial so-called standard electromagnetic quantities, which constitute the stress data, and which are stored to be used in the method for characterizing the environment under test according to the 'invention. Over time, one of the three, or more of these materials show changes in electromagnetic magnitudes. The method according to the invention makes it possible to detect the variations by taking into account the stress data, and image(s) of the cross section of the medium under test.

The invention is not limited to the embodiments described above.

Other constraint data can be used, as well as other algorithms and/or other antenna systems.

The invention applies generally to the characterization and diagnosis of liquid and/or viscous mixtures.

Claims (22)

Method for characterizing a medium, using an inversion algorithm, at least one tomographic image of said medium previously acquired and at least one datum, called stress, representative of at least one standard quantity of said medium or medium(s) similar to said environment,
method in which said inversion algorithm is used to extract at least one piece of information from said at least one tomographic image, and
at least one characteristic quantity of at least one property of said medium is determined from said at least one item of information extracted and by using said inversion algorithm of which at least one parameter is modified as a function of said at least one constraint datum. Method according to the preceding claim, in which said at least one parameter of the inversion algorithm is replaced by said at least one constraint datum. Method according to claim 1 or 2, in which several previously acquired images are used to form an information sequence also comprising the constraint data item(s), in particular by concatenation, said information sequence being used for determining said at least a magnitude characteristic of at least one property of said medium, the information sequence being in particular obtained by “ deep learning ” learning. Method according to any one of the preceding claims, in which the standard quantity(s) of the medium are maps or images of said medium or of medium(s) similar to said medium, or experimental values associated with said at least one property of the medium or similar medium(s). Process according to any one of the preceding claims, in which the property of the medium being a physico-chemical quantity chosen from among the concentration, the temperature, the pressure, the viscosity, the speed of flow of a liquid passing through the medium. Method according to one of the preceding claims, in which the characteristic quantity is an electromagnetic quantity such as the dielectric permittivity or the magnetic permeability. Method according to any one of Claims 1 to 5, in which the characteristic quantity is a physiological parameter. Process according to the preceding claim, in which the physiological parameter is blood sugar. Method according to the preceding claim, in which at least one piece of information from the image of the section of an arm and the stress data representative of dielectric quantities of healthy tissue(s) are used to determine a value of blood sugar, the inversion algorithm being constrained by the constraint data or data to converge towards the measurement of said blood sugar. A method according to claim 7, wherein the physiological parameter is blood lactate level. Method according to the preceding claim, in which at least one piece of information from the image of the section of an arm and the stress data representative of dielectric quantities of healthy tissue(s) are used to determine a value of lactate, the inversion algorithm being constrained by the constraint data or data to converge towards the measurement of said level of lactate in the blood. Process according to any one of Claims 1 to 6, in which the characteristic quantity is the level of a polluting product in an extraction medium, in particular a liquid, an object or a soil. Method according to the preceding claim, in which the said at least one constraint datum is a dielectric quantity or the value of a property of the extraction medium or of similar medium(s), such as temperature, pressure, or flow velocity. Process according to Claim 12 or 13, in which the polluting product is water and the extraction medium is a hydrocarbon, in particular in a pipe. System (1) for characterizing a medium under test, for implementing the method according to any one of the preceding claims, the system comprising:

• a network of tomographic sensors (2) connected to the medium under test,
• a switch box (5) connected to the sensors (2), and
• a processing unit comprising an integrated circuit configured to execute an inversion algorithm, to extract at least one piece of information from said at least one tomographic image by means of said inversion algorithm, and to determine a characteristic quantity of at least one property of said medium from said at least one item of information extracted and using said inversion algorithm of which at least one parameter is modified as a function of at least one datum, called constraint, representative of at least one standard quantity of said medium or medium(s) similar to said medium.

System according to the preceding claim, in which the integrated circuit is configured to replace the said at least one parameter of the inversion algorithm by the said at least one constraint datum. System according to Claim 15 or 16, in which the sensors (2) are electromagnetic transducers, in particular very near-field antennas. System according to the preceding claim, in which the transducers comprise transmitters and/or receivers. System according to any one of Claims 15 to 18, in which the switching box (5) comprises switches ensuring that the same transducer can be sometimes a transmitter and sometimes a receiver. System according to any one of Claims 15 to 19, in which the processing unit (7) is configured to create an information sequence formed by the images originating from the network of sensors (2) and the constraint data or data , said information sequence being used for determining said quantity characteristic of at least one property of the medium. System according to any one of claims 15 to 20, in which the network of sensors is attached to a peripheral support around a part of the body, in particular an armband (3) conforming to the shape of the arm, which the user wears to monitor the variations of a physiological parameter of his body. Computer program product comprising program code instructions recorded on a computer-readable medium for carrying out steps of the method as defined in any one of claims 1 to 14, when said program is executed on a computer .