EP2454601A1 - Procédé et ensemble pour la reconstitution de la source d'un champ électromagnétique - Google Patents

Procédé et ensemble pour la reconstitution de la source d'un champ électromagnétique

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Publication number
EP2454601A1
EP2454601A1 EP10749757A EP10749757A EP2454601A1 EP 2454601 A1 EP2454601 A1 EP 2454601A1 EP 10749757 A EP10749757 A EP 10749757A EP 10749757 A EP10749757 A EP 10749757A EP 2454601 A1 EP2454601 A1 EP 2454601A1
Authority
EP
European Patent Office
Prior art keywords
source
measuring space
electromagnetic field
measuring
electromagnetic
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Ceased
Application number
EP10749757A
Other languages
German (de)
English (en)
Inventor
Ludger Klinkenbusch
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
Christian Albrechts Universitaet Kiel
Original Assignee
Christian Albrechts Universitaet Kiel
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by Christian Albrechts Universitaet Kiel filed Critical Christian Albrechts Universitaet Kiel
Publication of EP2454601A1 publication Critical patent/EP2454601A1/fr
Ceased legal-status Critical Current

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Classifications

    • GPHYSICS
    • G01MEASURING; TESTING
    • G01RMEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
    • G01R29/00Arrangements for measuring or indicating electric quantities not covered by groups G01R19/00 - G01R27/00
    • G01R29/08Measuring electromagnetic field characteristics
    • G01R29/10Radiation diagrams of antennas
    • AHUMAN NECESSITIES
    • A61MEDICAL OR VETERINARY SCIENCE; HYGIENE
    • A61BDIAGNOSIS; SURGERY; IDENTIFICATION
    • A61B5/00Measuring for diagnostic purposes; Identification of persons
    • A61B5/24Detecting, measuring or recording bioelectric or biomagnetic signals of the body or parts thereof
    • A61B5/242Detecting biomagnetic fields, e.g. magnetic fields produced by bioelectric currents
    • A61B5/245Detecting biomagnetic fields, e.g. magnetic fields produced by bioelectric currents specially adapted for magnetoencephalographic [MEG] signals
    • A61B5/246Detecting biomagnetic fields, e.g. magnetic fields produced by bioelectric currents specially adapted for magnetoencephalographic [MEG] signals using evoked responses
    • AHUMAN NECESSITIES
    • A61MEDICAL OR VETERINARY SCIENCE; HYGIENE
    • A61BDIAGNOSIS; SURGERY; IDENTIFICATION
    • A61B5/00Measuring for diagnostic purposes; Identification of persons
    • A61B5/68Arrangements of detecting, measuring or recording means, e.g. sensors, in relation to patient
    • A61B5/6801Arrangements of detecting, measuring or recording means, e.g. sensors, in relation to patient specially adapted to be attached to or worn on the body surface
    • A61B5/6813Specially adapted to be attached to a specific body part
    • A61B5/6814Head

Definitions

  • the invention relates to a method for reconstructing the source of an electromagnetic field.
  • the invention also relates to an arrangement for carrying out the method.
  • the properties of an electromagnetic field within a closed space can only be determined exactly if certain properties of the electromagnetic field are known on a surface completely enclosing the space. The exact determinability is independent of whether there is a source of the electromagnetic field in the closed space area or not.
  • the laws of electrodynamics are based on the requirement of a continuous and comprehensive knowledge of the properties of the electromagnetic field on the surface completely enclosing the space area. In technical applications, this requirement is not met regularly.
  • a plurality of sensors are placed on the surface.
  • the information obtained by the sensors about the properties of the electromagnetic field on the surface is discrete.
  • an unambiguous determination of the electromagnetic field in the spatial area is possible, but different from continuous measured values are no longer exact, but only within a fault barrier.
  • an electromagnetic field in a closed spatial area is uniquely determined by recording measured values on its surface, this always means a determination that is unambiguous within the scope of the error barrier.
  • Such measurements are made, for example, to determine the characteristics of an antenna.
  • measuring sensors are uniformly distributed on a surface completely enclosing the antenna, for example a spherical surface, and measured values relating to properties of the electromagnetic field radiated by the antenna are recorded.
  • a mathematical model of the antenna is set up and a field development of the electromagnetic field radiated by the antenna is carried out, the coefficients of the field development being initially unknown.
  • the unknowns of field development are related to the measurements taken by the probes.
  • the properties of the antenna can be unambiguously calculated within the error bound caused by the discretion of the measured values (J.E. Hansen (Ed.), Spherical Near-Field Antenna Measurements, Peter Peregrinus Ltd., 1988).
  • a surface that does not completely surround the sources exists in particular in the case of measurements made on the human body in the context of magnetoencephalography or magnetocardiography.
  • Magnetoencephalography measures the magnetic field around the head and reconstructs the brain waves that are the source of the magnetic field.
  • Magnetocardiography attempts in a similar way to deduce the causative cardiac currents from magnetic fields in the vicinity of the trunk. In both cases, sensors would have to be placed inside the human body to measure the magnetic field on a surface completely surrounding the source.
  • the invention is based on the above-mentioned prior art, the object to provide a method and an arrangement for reconstructing the source of an electromagnetic field, which are associated with a lower uncertainty.
  • the object is solved by the features of the independent claims. Advantageous embodiments can be found in the subclaims.
  • a source is separated from the source Selected measuring room, so that the measuring room is connected via a magnetically homogeneous space area with the source.
  • Measured values of the electromagnetic field emitted by the source are recorded on the surface of the measuring space.
  • the measured values are recorded in such a way that the electromagnetic field can be unambiguously determined within the scope of a fault barrier caused by the discretion of the measured values.
  • a mathematical model of the source is developed which has a plurality of unknowns and a system of equations is set up which relates the unknowns of the model with the measured values. By solving the equation system, the properties of the electromagnetic source can be determined.
  • a plurality of measuring probes are provided for recording properties of the electromagnetic field emitted by the source, which are arranged on the surface of a measuring space separate from the source such that the electromagnetic field in the measuring space can be unambiguously determined within a fault limit caused by the discretion of the measured values.
  • the system further includes a computing module configured to solve a system of equations in which a plurality of unknowns of a model of the electromagnetic source are related to the measurements of the probes to determine the characteristics of the electromagnetic source.
  • a measurement space is then separate from the source of an electromagnetic field if the source is not contained in the measurement space.
  • a completely closed surface surrounding the measuring space is at a distance from the source.
  • a beam emanating from the center of the electromagnetic source towards the measurement space intersects the surface of the measurement space more than once.
  • One Space area is referred to as magnetically homogeneous when the magnetic permeability within the space is substantially constant. This applies, for example, to media such as vacuum, air and biological tissue. Magnetic homogeneity is sufficient if direct currents are to be reconstructed as sources of a magnetic field. If the source of an electromagnetic field is to be reconstructed, then the spatial area must be electromagnetically homogeneous.
  • a space region is said to be electromagnetically homogeneous when the electrical permittivity, electrical conductivity and magnetic permeability within the space are substantially constant. This applies, for example, to vacuum and air.
  • the properties of the electromagnetic field measured on the surface of the measuring space are those which, according to the laws of electrodynamics, permit a definite reconstruction of a specific source of the electromagnetic field if they are continuously known on a surface completely enclosing the source.
  • the characteristics of the electromagnetic field in individual cases depend on the type of source. If, for example, the electrical currents that form the source of a magnetic field are to be reconstructed, then either the knowledge of the tangential component of the magnetic field or the knowledge of the normal component of the magnetic field on the surface is required.
  • Reconstruction of the antenna current as the source of an electromagnetic field requires knowledge of the tangential component of the electric field or the tangential component of the magnetic field on a surface completely enclosing the antenna. If the electromagnetic field is static, it is sufficient to measure the properties at a single point in time. Is this Electromagnetic field time varying, so the measurement must be designed so that it detects the passage of time. With a discrete-time recording of measured values, this means in particular that the sampling theorem should be satisfied. It is possible to record a large number of measured values or all measured values at different locations parallel to each other. In the case of static processes or periodic time dependency, the measured values at the different locations can be recorded one after the other in chronological order.
  • the brain waves as a source of a magnetic field can be modeled, for example, as a superposition of N electric dipoles (known as infinitesimal strands) at a known location and with known polarization but unknown amplitudes (S. Baillet et al., Electromagnetic Brain Mapping, IEEE Signal Processing Magazine, 14-30 , Nov. 2001).
  • the properties of the electromagnetic source are determined explicitly with such a model. As implied by the invention implied determination of the source, it is referred to, if only the electromagnetic field emitted by the source is determined so that the source is uniquely defined by the field.
  • the step of actually calculating the source from the field need not necessarily be performed within the scope of the invention.
  • the electromagnetic field mediated can be modeled as a superposition of N plane waves of known polarization but of unknown amplitude and phase.
  • the invention is based on a fundamental theorem that the inventor has recently developed and published (L. Klinkenbusch, Brief Review of Spherical-Multipole Analysis in Radio Science, Radio Science Bulletin, 324 (March 2008), 5-16). Thereafter, the electromagnetic field is uniquely determined in an electromagnetically homogeneous region, as long as the electric or magnetic field is known at any point and its infinitesimal environment in that region.
  • the theorem is directly applicable to purely magnetic fields as follows Apply: The magnetic field in a magnetically homogeneous area is uniquely determined as long as the magnetic field is known at any point and its infinitesimal environment in that area.
  • the theorem is used for a specific technical application, namely the determination of the source of an electromagnetic field from field components obtained by measurement.
  • the error barrier caused by the discretion of the measured values for the determination of the electromagnetic field in the measuring space can be quantified, for example in the form of a local quadratic error.
  • the electromagnetic field can be determined as accurately anywhere in the measurement space then the * s is the local square error below the error bound.
  • Whether an arrangement of measuring probes on the surface of the measuring chamber with respect to a certain error barrier satisfies the condition that the electromagnetic field in the measuring space can be unambiguously determined within the error barrier can be calculated analytically in geometrically simple arrangements.
  • a geometrically simple arrangement in this sense is given, for example, if the measuring space has a spherical shape (JE Hansen
  • the procedure is preferably such that an error limit is determined and analytically, a distribution of sensors on the surface of the measuring space is determined based on the error barrier, which satisfies the condition.
  • a high-resolution finite element simulation can first be used to calculate a reference field in the measurement space which belongs to an assumed continuous distribution of the measured values. (Jin, The Finite Element Method in Electro- mics, John Wiley & Sons, 1993). The surface of the measurement space is then divided into individual non-overlapping elements so that the sum of these elements covers the entire surface and that of each surface element a measuring sensor, ie a measured value of the assumed continuous distribution is assigned.
  • an error bound is first defined and then by means of the approximation method a distribution of Determined sensors on the surface of the measuring chamber, so that the electromagnetic field in the measuring space within the error barrier is uniquely determined.
  • both the analytical and the approximate calculations will lead to an array of probes that are essentially equally distributed on the surface of the measurement space.
  • the goal of the method according to the invention is not the determination of the electromagnetic field in the measuring space, but the reconstruction of the electromagnetic source.
  • the error bound in the measurement space does not match the error within which the electromagnetic source can be reconstructed.
  • the error barrier from the measurement space propagates through the system of equations and causes the error barrier at the electromagnetic source to be larger.
  • there is a one-to-one correspondence between the error barrier in the measuring room and the fault barrier of the electromagnetic source which, however, can not be calculated analytically in all cases.
  • the error propagation from the error barrier of the measurement space to the error barrier of the electromagnetic source depends essentially on how the measurement space is related to the electromagnetic field. see source is arranged. Generally, it will be said that the error propagation becomes smaller when the measurement space is closer to the electromagnetic source.
  • the distance between the probes and the electromagnetic source must not be too small, so that no feedback occurs.
  • a suitable distance between the measuring chamber and the electromagnetic source must be determined individually for each measuring problem.
  • magneto-encephalography and magnetocardiography the probes are outside the body and are thus automatically spaced from the source. It is useful in these measurements to arrange the sensors in the immediate vicinity of the body. For measurements on antennas, one can orientate on the distance that is selected in classical measuring methods.
  • the solid angle of the closed spherical surface is known to be 4 ⁇ .
  • the measuring space preferably covers 1/6, more preferably 1/3, further preferably 1/2, more preferably 2/3 relative to the center of the electromagnetic source. Within this solid angle, the condition is to be fulfilled that a beam emanating from the center of the electromagnetic source intersects the measuring space at least twice.
  • the surface of the measuring space may comprise a first surface portion and a second surface portion, which are arranged substantially parallel to each other and together make up more than 50%, preferably more than 70%, more preferably more than 80% of the total surface of the measuring space.
  • the two surface portions may be oriented such that a beam emanating from the electromagnetic source is incident both on the first surface part as well as the second area proportion cuts.
  • the first area portion may have a concave shape and the second area portion may have a convex shape with the concave area portion oriented toward the source.
  • the measuring space has the shape of a cylindrical shell or a segment of a spherical shell, in the center of which the electromagnetic source is arranged.
  • the thickness of the measuring space ie the distance between the point at which the
  • the thickness of the measuring space is preferably at least 0.5 times as large, more preferably at least as great, more preferably at least twice as large as the distance between the source and the measuring space.
  • Such a large thickness of the measuring space will be selected, in particular, even if a good signal strength is still present at the far end of the measuring chamber. This is the case, for example, when surveying antennas.
  • the signal strength is low, as in magnetoencephalography and in magneto-cardiography, a small thickness of the measurement space will be selected in order to obtain usable readings even at the far end of the measurement space.
  • the thickness of the measuring space is then preferably less than 1/2, more preferably less than 1/3, more preferably less than 1/5 of the distance between the center of the source region and the measuring space. If the electromagnetic source is described by a multipole development, a small thickness of the measurement space leads to a high sensitivity with respect to the higher terms of the development.
  • Fig. 1 a schematic representation of an antenna and an inventive arrangement
  • Figures 2 to 4 the view of Figure 1 in other embodiments of the invention.
  • FIG. 5 shows a cross section through an antenna and a measuring chamber
  • Fig. 6 the view of Figure 5 in another embodiment of the invention.
  • Fig. 7 an inventive arrangement in application in a
  • FIG. 8 shows an arrangement according to the invention in application in a
  • N probes 12 are uniformly distributed on a cuboid surface.
  • the space area surrounded by the probes 12 is referred to as the measuring space 14.
  • the electromagnetic field in the measuring space 14 can be unambiguously determined. Using the described finite element method, it can be calculated within which error barrier the determination of the electromagnetic field in the measuring space 14 is unambiguous.
  • the N probes 12 are designed to measure each amplitude and phase of the electromagnetic field. The measured values are transmitted from the measuring sensors 12 to a computer 16 via signal lines 15.
  • an antenna 10 shown schematically in FIG. 1 is arranged, which in this case is a directional antenna and emits electromagnetic radiation, preferably in the direction of the measuring space 14.
  • the space between the measuring space 14 and the antenna 10 is electromagnetically homogeneous.
  • a superposition of N levels of electromagnetic waves of known polarization is assumed.
  • Known is the origin of the electromagnetic waves, which coincides with the location of the antenna 10.
  • Unknown are the phase and amplitude of the plane waves.
  • This mathematical model of the electromagnetic radiation emitted by the antenna 10 is stored in the computer 16.
  • a system of equations is stored in the computer 16, by means of which the unknowns of the model are related to the measured values of the sensors 12.
  • the 2 * N unknowns are compared with the measured values of the N probes 12, which respectively measure the amplitude and phase of the electromagnetic field, 2 * N measured values. It follows from the theorem underlying the invention that this system of equations has a definite solution.
  • the computer 16 determines this solution according to known numerical methods. As a result, one obtains unique values for the coefficients of field development.
  • the electromagnetic field emitted by the antenna 10 is clearly reconstructed within the framework of a definable error barrier. In particular, it is now possible to calculate the far field of the antenna 10.
  • the properties of the antenna 10 itself are also uniquely determined. If you do the corresponding calculation? neuter perform, so the properties of the antenna 10 would be determined explicitly. If one waives this calculation, the properties of the antenna 10 are only implicitly known.
  • all N probes 12 simultaneously record measured values of the electromagnetic field. If the electromagnetic field has a time-repeating course, this is not necessary, but the measured values can also be obtained successively.
  • An arrangement designed to acquire the measured values in succession is shown in FIG.
  • a sensor 17 is mounted on a vehicle 19 via a telescopic mechanism 18. The sensor 17 moves successively N certain points on the surface of the indicated by dashed lines measuring space 14 and there takes each measured values of phase and amplitude of the emitted from the antenna 10 electric field. In the sum of all measured values, the information is exactly the same as that of the measured values recorded in FIG. 1, so that an identical calculation can be carried out.
  • a superimposition of N multipoles is selected as the mathematical model of the antenna 10.
  • the location of the N multipole coincides with the location of the antenna 10, so it is known.
  • the electromagnetic field in a measuring space 14 which has a distance a from the antenna 10, must be able to be unambiguously determinable within a fault barrier.
  • the size of the error barrier in measuring space 14 can be estimated using known mathematical methods. If in this way a concrete value for the error barrier in the measuring space is available, a suitable form of the measuring space for the specific problem can first be selected and subsequently a suitable distribution of measuring sensors on the surface of the measuring space can be determined.
  • a spherical measuring space proves to be suitable for the problem.
  • the shape of the measuring space 14 is indicated in FIG. 3 by a solid line.
  • N an arrangement of N on the surface of the spherical measuring space 14 is equally distributed to probes 12 in order to unambiguously determine the electromagnetic field in the measuring space 14 within the predetermined error barrier. If this information is available, the practical implementation can be stepped on by first distributing the N probes 12 on the surface of the spherical measuring space 14 according to the calculation.
  • the probes 12 are designed to each measure the tangential component of the electric field.
  • the antenna 10 is modeled as in Fig. 3 as a superposition of N multipoles.
  • it can be estimated within which error barrier the electromagnetic field in the measuring space 14 must be unambiguously determinable so that the coefficients of the multipole development can be determined with a desired accuracy.
  • the irregularly shaped measuring space 14 of FIG. 4 it can not be analytically calculated from the given error barrier how the measuring sensors 12 are to be distributed on the surface of the measuring space 14, so that the condition is met.
  • it is possible to determine the distribution of the probes 12 by an approximation method such as the finite element method. For this purpose, an arbitrary distribution of sensors is assumed and checked, whether with this distribution the field in the measurement space within the error barrier is uniquely determined.
  • the sensors 12 measure either the tangential component of the electrical or the tangential component of the magnetic field. In Fig. 4, both components are measured. If the determination of the electromagnetic field on the basis of these measured values is carried out twice independently of one another, the results can be compared with one another, so that an error correction is possible.
  • the antenna 10 emits omnidirectional electromagnetic radiation.
  • the shape of the measuring space 14 corresponds to a segment of a spherical shell which almost completely surrounds the antenna 10.
  • the spherical shell has an inner concave surface portion 20 and an outer convex surface portion 21. Together, the concave surface portion 20 and the convex surface portion 21 make up more than 80% of the surface of the measuring space 14.
  • the thickness d of the measuring space 14 corresponds to the distance a between the antenna 10 and the inner concave surface portion 20.
  • the solid angle in which the antenna 10 is surrounded by the measuring space 14 corresponds to more than 90% of the full sphere. With this design it offers to perform a spherical Multipolgraphy for the antenna 10.
  • An antenna with a complex directional characteristic is characterized by a relatively large L. For given L must total
  • the associated spatial frequency spectrum ie the multipole amplitudes of the associated interference field
  • Gig. (1) the total calculated multipole amplitudes due to the linearity of the medium. Accordingly, a calibration of the measuring arrangement is thereby possible, initially a measurement without the useful sources (eg in the case of Magnetoencephalography without patients) and deduct the multipole amplitudes thus determined from the total measured.
  • the antenna 10 is an omnidirectional antenna.
  • the measuring space 14 has the shape of a cylindrical shell, in the center of which the antenna 10 is arranged. The bottom and top of the cylindrical shape are not part of the measuring space 14.
  • the measuring space 14 here also includes a concave inner surface 20 and a convex outer surface 21.
  • the thickness d of the measuring space 14 is small compared to the distance a meanwhile the antenna 10 and the concave inner surface 20th In this problem, the model of the antenna 10 will be developed according to cylinder-wave functions.
  • Fig. 7 shows an application of the invention in magnetoencephalography.
  • the brain electrical currents 23 in the head 22 of a patient are to be determined, which are the source of a magnetic field measured in the vicinity of the head 22.
  • the brain waves 23 are indicated in Fig. 7 with arrows.
  • a measuring space 14, which has the shape of a segment of a spherical shell, is arranged so that it surrounds the head 22 of the patient as closely as possible.
  • the space between the measuring space 14 and the brain streams 23 contains different media, namely air and biological tissue.
  • the media have a substantially identical magnetic permeability, so that the measuring space 14 in the context of the invention is connected to the brain streams 23 via a magnetically homogeneous spatial area. Since the signal strength is low in this type of measurement, the measuring space 14 has a small thickness d.
  • Each of these dipoles generates one magnetic flux density B calculated according to the law of Biot-Savart in place r k according to
  • Magnetic field B (r fc ) in each case only know the tangentially or normally directed with respect to the measuring surface field components. Let's assume here that only the normal field components
  • n in the matrix elements should symbolize the sole consideration of the normal components.
  • the desired amplitudes of the dipoles are now determined by suitable methods from the linear algebra by solving the linear equation system.
  • r k can be tried with different varieties adopted to solve the system of equations.
  • An unambiguous solution of the equation system exists according to the theorem on which the invention is based, if and only if the locations r k are correctly assumed. There is thus the possibility to determine iteratively the right places r k.
  • the invention is applied in the context of a Magnetokardi- ographie.
  • the purpose of this application is to identify the cardiac currents as the source of a magnetic field.
  • Shown schematically is a trunk 24 of a patient with indicated cardiac currents 25.
  • measurements of the normal or tangential component of the magnetic field on the surface of the measurement space 14 can be used to deduce the cardiac currents, which are modeled as an overlay of N dipoles.

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  • Health & Medical Sciences (AREA)
  • Physics & Mathematics (AREA)
  • Life Sciences & Earth Sciences (AREA)
  • Biomedical Technology (AREA)
  • Medical Informatics (AREA)
  • Biophysics (AREA)
  • Pathology (AREA)
  • Engineering & Computer Science (AREA)
  • Electromagnetism (AREA)
  • Heart & Thoracic Surgery (AREA)
  • General Physics & Mathematics (AREA)
  • Molecular Biology (AREA)
  • Surgery (AREA)
  • Animal Behavior & Ethology (AREA)
  • General Health & Medical Sciences (AREA)
  • Public Health (AREA)
  • Veterinary Medicine (AREA)
  • Measurement And Recording Of Electrical Phenomena And Electrical Characteristics Of The Living Body (AREA)

Abstract

L'invention concerne un procédé de reconstitution de la source (10, 23, 25) d'un champ électromagnétique, comprenant, tout d'abord, la sélection d'un espace de mesure (14) distinct de la source (10, 23, 25) de telle façon que la chambre de mesure (14) soit reliée à la source (10, 23, 25) par une zone de mesure magnétiquement homogène; puis l'enregistrement sur la surface de la zone de mesure (14) des valeurs de mesure du champ électromagnétique émises par la source (10, 23, 25) de façon à déterminer de manière univoque le champ électromagnétique dans l'espace de mesure dans les limites d'une borne d'erreur due à la discrèteté des valeurs de mesure; la détermination d'un modèle mathématique de la source électromagnétique (10, 23, 25), ledit modèle présentant une pluralité d'inconnues, et la présentation d'un système d'équations qui met en relation les inconnues du modèle et les valeurs de mesure. La résolution du système d'équations permet de déterminer les propriétés de la source électromagnétique (10, 23, 25). L'invention concerne également un ensemble pour la mise en oeuvre dudit procédé. Le procédé selon l'invention, l'insécurité est réduite lors de la reconstitution de sources électromagnétiques.
EP10749757A 2009-07-16 2010-07-14 Procédé et ensemble pour la reconstitution de la source d'un champ électromagnétique Ceased EP2454601A1 (fr)

Applications Claiming Priority (2)

Application Number Priority Date Filing Date Title
DE102009033421A DE102009033421A1 (de) 2009-07-16 2009-07-16 Verfahren und Anordnung zum Rekonstruieren der Quelle eines elektromagnetischen Feldes
PCT/DE2010/000824 WO2011006480A1 (fr) 2009-07-16 2010-07-14 Procédé et ensemble pour la reconstitution de la source d'un champ électromagnétique

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EP2454601A1 true EP2454601A1 (fr) 2012-05-23

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EP (1) EP2454601A1 (fr)
DE (1) DE102009033421A1 (fr)
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US20120116725A1 (en) 2012-05-10
WO2011006480A1 (fr) 2011-01-20
US8954293B2 (en) 2015-02-10

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