WO2011121487A1 - Appareil et procédé de formation d'une image de la concentration de particules magnétiques disposées dans un champ de vue - Google Patents

Appareil et procédé de formation d'une image de la concentration de particules magnétiques disposées dans un champ de vue Download PDF

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Publication number
WO2011121487A1
WO2011121487A1 PCT/IB2011/051213 IB2011051213W WO2011121487A1 WO 2011121487 A1 WO2011121487 A1 WO 2011121487A1 IB 2011051213 W IB2011051213 W IB 2011051213W WO 2011121487 A1 WO2011121487 A1 WO 2011121487A1
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field
detection signals
magnetic
view
approximation
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PCT/IB2011/051213
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English (en)
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Hermann Schomberg
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Koninklijke Philips Electronics N.V.
Philips Intellectual Property & Standards Gmbh
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Publication of WO2011121487A1 publication Critical patent/WO2011121487A1/fr

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    • A—HUMAN NECESSITIES
    • A61—MEDICAL OR VETERINARY SCIENCE; HYGIENE
    • A61B—DIAGNOSIS; SURGERY; IDENTIFICATION
    • A61B5/00—Measuring for diagnostic purposes; Identification of persons
    • A61B5/05—Detecting, measuring or recording for diagnosis by means of electric currents or magnetic fields; Measuring using microwaves or radio waves 
    • A—HUMAN NECESSITIES
    • A61—MEDICAL OR VETERINARY SCIENCE; HYGIENE
    • A61B—DIAGNOSIS; SURGERY; IDENTIFICATION
    • A61B5/00—Measuring for diagnostic purposes; Identification of persons
    • A61B5/05—Detecting, measuring or recording for diagnosis by means of electric currents or magnetic fields; Measuring using microwaves or radio waves 
    • A61B5/0515—Magnetic particle imaging
    • A—HUMAN NECESSITIES
    • A61—MEDICAL OR VETERINARY SCIENCE; HYGIENE
    • A61B—DIAGNOSIS; SURGERY; IDENTIFICATION
    • A61B5/00—Measuring for diagnostic purposes; Identification of persons
    • A61B5/72—Signal processing specially adapted for physiological signals or for diagnostic purposes
    • A61B5/7235—Details of waveform analysis
    • A61B5/7253—Details of waveform analysis characterised by using transforms
    • A61B5/7257—Details of waveform analysis characterised by using transforms using Fourier transforms

Definitions

  • the present invention relates to an apparatus and a method for forming a concentration image of the concentration of magnetic particles arranged in a field of view. Further, the present invention relates to a computer program for implementing said method on a computer and for controlling such an apparatus. The present invention relates particularly to the field of Magnetic Particle Imaging.
  • Magnetic Particle Imaging is an emerging medical imaging modality.
  • the first versions of MPI were two-dimensional in that they produced two-dimensional images. Future versions will be three-dimensional (3D).
  • a four-dimensional image of a non-static object can be created by combining a temporal sequence of 3D images to a movie, provided the object does not significantly change during the data acquisition for a single 3D image.
  • MPI is a reconstructive imaging method, like Computed Tomography or Magnetic Resonance Imaging. Accordingly, an MP image of an object's volume of interest is generated in two steps.
  • the first step referred to as data acquisition, is performed using an MPI scanner.
  • the MPI scanner has means to generate a static magnetic gradient field, called the "selection field", which has a single field- free point (FFP) at the isocenter of the scanner. Moreover, this FFP is surrounded by a first sub-zone with a low magnetic field strength, which is in turn surrounded by a second sub-zone with a higher magnetic field strength.
  • the scanner has means to generate a time-dependent, spatially nearly homogeneous magnetic field.
  • this field is obtained by superposing a rapidly changing field with a small amplitude, called the "drive field”, and a slowly varying field with a large amplitude, called the "focus field”.
  • the FFP may be moved along a predetermined FFP trajectory throughout a
  • volume of scanning surrounding the isocenter.
  • the scanner also has an arrangement of one or more, e.g. three, receive coils and can record any voltages induced in these coils.
  • the object to be imaged is placed in the scanner such that the object's volume of interest is enclosed by the scanner's field of view, which is a subset of the volume of scanning.
  • the object must contain magnetic nanoparticles; if the object is an animal or a patient, a contrast agent containing such particles is administered to the animal or patient prior to the scan.
  • the MPI scanner steers the FFP along a deliberately chosen trajectory that traces out the volume of scanning, or at least the field of view.
  • the magnetic nanoparticles within the object experience a changing magnetic field and respond by changing their magnetization.
  • the changing magnetization of the nanoparticles induces a time-dependent voltage in each of the receive coils. This voltage is sampled in a receiver associated with the receive coil.
  • the samples output by the receivers are recorded and constitute the acquired data.
  • the parameters that control the details of the data acquisition make up the "scan protocol".
  • the image is computed, or reconstructed, from the data acquired in the first step.
  • the image is a discrete 3D array of data that represents a sampled approximation to the position-dependent concentration of the magnetic nanoparticles in the field of view.
  • the reconstruction is generally performed by a computer, which executes a suitable computer program.
  • Computer and computer program realize a reconstruction algorithm.
  • the reconstruction algorithm is based on a mathematical model of the data acquisition. As with all reconstructive imaging methods, this model can be formulated as an integral operator that acts on the acquired data; the reconstruction algorithm tries to undo, to the extent possible, the action of the model.
  • Such an MPI apparatus and method have the advantage that they can be used to examine arbitrary examination objects - e. g. human bodies - in a non-destructive manner and with a high spatial resolution, both close to the surface and remote from the surface of the examination object.
  • Such an apparatus and method are generally known and have been first described in DE 101 51 778 Al and in Gleich, B. and Weizenecker, J. (2005),
  • the detection signals used in the reconstruction are subjected to high-pass filtering (e.g. with a cut-off frequency of 25 kHz) before reconstruction processing to suppress (comparably strong) signal components, which do not result from the magnetic particles themselves but from the applied magnetic field itself or from drive field coils which also serve as receive coils.
  • high-pass filtering e.g. with a cut-off frequency of 25 kHz
  • the high-pass filtering adversely affects the quality of the reconstructed images since information this filtering also cuts off signal components below the cut-off frequency that are actually generated by the magnetic particles. In other words, some useful signal is lost according to this conventionally applied method.
  • selection means comprising a selection field signal generator unit and selection field elements for generating a magnetic selection field having a pattern in space of its magnetic field strength such that a first sub-zone having a low magnetic field strength and a second sub-zone having a higher magnetic field strength are formed in the field of view
  • drive means comprising drive field signal generator units and drive field coils for changing the position in space of the two sub-zones in the field of view by means of a magnetic drive field so that the magnetization of the magnetic material changes locally
  • - receiving means comprising at least one signal receiving unit and at least one receiving coil for acquiring detection signals, which detection signals depend on the magnetization in the field of view, which magnetization is influenced by the change of the position in space of the first and second sub-zone
  • said reconstruction means is adapted for determining said corrected detection signals from i) actual detection signals acquired at different positions of the first sub-zone with the magnetic particles arranged in the field of view, ii) calibration detection signals acquired at different positions of the first sub-zone with no magnetic particles arranged in the field of view, and iii) approximation detection signals determined as an approximation to said calibration detection signals,
  • said corrected detection signals are obtained by subtracting the difference between said calibration detection signals and said approximation detection signals from the difference between said actual detection signals and said approximation detection signals.
  • the present invention has for its aim to overcome the need to subject the acquired detection signal (called “actual detection signals” hereinafter) to high-pass filtering prior to further processing, in particular for reconstructing an image, by subtracting calibration detection signals from the actual detection signals, which calibration detection signals are acquired in advance with an empty apparatus, i.e. without any object or magnetic particles being placed in the field of view.
  • an empty apparatus i.e. without any object or magnetic particles being placed in the field of view.
  • the first option is applied in a one-time calibration step.
  • the intermediate differential signals are generated before the sampling, i.e. in analog form, whereas the subtraction of the intermediate differential signals from each other is done after sampling the intermediate differential signals, i.e. in digital form.
  • the approximation detection signals are thus generated on the fly and are reproducibly reproduced.
  • the approximation detection signals should thus be provided in sampled form and during the actual measurement of actual detection signals, analog versions should be obtained therefrom on the fly by D/A conversion.
  • the sampled values of the approximation detection signals can be obtained, for instance by A/D conversion (using a moderate number of bits and, for instance, a conventional A/D converter) from the calibration detection signals obtained by the calibration measurement.
  • the calibration detection signals can also be calculated ("simulated"). This can be done by calculating the applied field, i.e. the sum of the selection, drive, and ( if used) focus fields, by applying the Biot-Savart law using knowledge about the geometry of the coils and the currents flowing through the coils. Then, the magnetic flux is calculated which is generated by the applied magnetic field in the receive coils. Next, the negative time derivative of the magnetic flux is calculated. Finally, an m-bit step function is made from the simulated signal, whose step heights are represented by m bits for the intended D/A conversion (m should thus be adapted to the abilities of the D/A converter).
  • the apparatus is adapted for acquiring said calibration detection signals at the same different positions of the first sub-zone with no magnetic particles arranged in the field of view at which the actual detection signals are acquired.
  • the same trajectory of the FFP or, more generally, the same scan protocol (i.e. the same trajectory and the same sampling pattern) is used as for acquiring the actual detection signals, which ensures that both data sets are available with the same sampling pattern and that the calibration detection signals correctly reflect the influence of (only) the exciting magnetic field.
  • the apparatus is adapted for acquiring said calibration detection signals before said actual detection signals are acquired. This enables the acquisition of various sets of calibration detection signals for a particular apparatus, in particular for various FFP trajectories. Later, after an actual acquisition of actual detection signals, the correct set, e.g. the set that has been acquired with the same FFP trajectory as the actual set of actual detection signals, is then selected and used in the subsequent
  • the apparatus comprises a storage means for storing said approximation detection signals and/or a storage means for storing said differences between said actual detection signals and said calibration detection signals and between said approximation detection signals and said calibration detection signals.
  • the one set or, preferably, more sets of said difference between said calibration detection signals and said approximation detection signals are then stored and can be reused later as needed.
  • the calibration detection signals are newly and individually acquired for immediate subsequent use, or that this is generally done each time when actual detection signals are acquired for image reconstruction.
  • the apparatus further comprises approximation means for determining said approximation detection signals by a simulation, in particular by application of the Biot-Savart law describing the magnetic field generated by an electric current flowing through a coil, and by applying an m-bit AD conversion on the simulated signals.
  • the apparatus is adapted for determining said approximation detection signals by applying an m-bit AD conversion, e.g. by use of an m-bit AD converter, to the calibration detection signals.
  • an m-bit AD conversion e.g. by use of an m-bit AD converter
  • the dynamic range of the difference signal is reduced by m bits.
  • the approximation detection signals can also be stored and no separate means for measuring them needs to be provided.
  • the reconstruction means can generally be implemented in various way, e.g. by hard- and/or software, for instance by use of a processor.
  • the apparatus further comprises analog-to-digital conversion means for converting digital approximation detection signals to analog approximation detection signals, and analog-to-digital conversion means for converting said differences into digital signals before subtracting said differences from each other for determining said corrected detection signals.
  • the analog difference signals have a lower dynamic range than the analog actual signals and analog calibration signals. This provides the advantage that the difference signals can be digitized by a conventional analog-to-digital converter with sufficient accuracy.
  • focus means are provided in an embodiment for changing the position in space of the field of view by means of a magnetic focus field. Such a focus field has the same (or similar) spatial distribution as the drive field. Separate (preferably) or the same means (e.g.
  • the focus means and the drive means can be used as the focus means and the drive means.
  • the frequencies are much lower (e.g. ⁇ 1 kHz, typically ⁇ 100 Hz) for the focus field that for the drive field, but the amplitudes of the focus field are much higher (e.g. 200 mT compared to 20 mT for the drive field).
  • These fields are used to move the FFP to a desired position.
  • the drive field is required in addition to the focus field since the detection signal obtainable with only the focus field would not be usable for the desired purpose, as the frequencies produced in the object of interest are much too low (typically ⁇ 10 kHz).
  • Fig. 1 shows a first embodiment of an MPI apparatus
  • Fig. 2 shows an example of the selection field pattern produced by an
  • Fig. 3 shows a second embodiment of an MPI apparatus
  • Fig. 4 shows a block diagram of an MPI apparatus according to the present invention
  • Fig. 5 shows an FFP trajectory for the first embodiment of the MPI apparatus
  • Fig. 6 shows an example of an FFP trajectory to be created by the focus field
  • Fig. 7 shows a graph of the Langevin function.
  • the first embodiment 10 of an MPI scanner shown in Fig. 1 has three pairs 12, 14, 16 of coaxial parallel circular coils, these coil pairs being arranged as illustrated in Fig. 1. These coil pairs 12, 14, 16 serve to generate the selection field as well as the drive and focus fields.
  • the axes 18, 20, 22 of the three coil pairs 12, 14, 16 are mutually orthogonal and meet in a single point, designated the isocenter 24 of the MPI scanner 10.
  • these axes 18, 20, 22 serve as the axes of a 3D Cartesian x-y-z coordinate system attached to the isocenter 24.
  • the vertical axis 20 is nominated the y-axis, so that the x- and z-axes are horizontal.
  • the coil pairs 12, 14, 16 are named after their axes.
  • the y-coil pair 14 is formed by the coils at the top and the bottom of the scanner.
  • the coil with the positive (negative) y-coordinate is called the y -coil (y -coil), and similarly for the remaining coils.
  • the coordinate axes and the coils shall be labelled with x l s x 2 , and x 3 , rather than with x, y, and z.
  • the scanner 10 can be set to direct a predetermined, time-dependent electric current through each of these coils 12, 14, 16, and in either direction. If the current flows clockwise around a coil when seen along this coil's axis, it will be taken as positive, otherwise as negative. To generate the static selection field, a constant positive current I s is made to flow through the z + -coil, and the current -I s is made to flow through the z -coil. The z-coil pair 16 then acts as an anti-parallel circular coil pair.
  • the magnetic selection field which is generally a magnetic gradient field, is represented in Fig. 2 by the field lines 50. It has a substantially constant gradient in the direction of the (e.g. horizontal) z-axis 22 of the z-coil pair 16 generating the selection field and reaches the value zero in the isocenter 24 on this axis 22. Starting from this field- free point (not individually shown in Fig. 2), the field strength of the magnetic selection field 50 increases in all three spatial directions as the distance increases from the field-free point.
  • first sub-zone or region 52 which is denoted by a dashed line around the isocenter 24 the field strength is so small that the magnetization of particles present in that first sub-zone 52 is not saturated, whereas the magnetization of particles present in a second sub-zone 54 (outside the region 52) is in a state of saturation.
  • the magnetic field strength of the selection field is sufficiently strong to keep the magnetic particles in a state of saturation.
  • the (overall) magnetization in the field of view 28 changes.
  • information about the spatial distribution of the magnetic particles in the field of view 28 can be obtained.
  • further magnetic fields i.e. the magnetic drive field, and, if applicable, the magnetic focus field, are superposed to the selection field 50.
  • a time dependent current I°i is made to flow through both x-coils 12, a time dependent current I D 2 through both y-coils 14, and a time dependent current I D 3 through both z-coils 16.
  • each of the three coil pairs acts as a parallel circular coil pair.
  • a time dependent current I F i is made to flow through both x-coils 12, a current I F 2 through both y-coils 14, and a current I F 3 through both z-coils 16.
  • the z-coil pair 16 is special: It generates not only its share of the drive and focus fields, but also the selection field.
  • the current flowing through the z ⁇ -coil is I D 3 + I F 3 ⁇ I s .
  • the selection field Being generated by an anti-parallel circular coil pair, the selection field is rotationally symmetric about the z-axis, and its z-component is nearly linear in z and independent of x and y in a sizeable volume around the isocenter 24.
  • the selection field has a single field- free point (FFP) at the isocenter.
  • FFP field- free point
  • the drive and focus fields which are generated by parallel circular coil pairs, are spatially nearly homogeneous in a sizeable volume around the isocenter 24 and parallel to the axis of the respective coil pair.
  • the drive and focus fields jointly generated by all three parallel circular coil pairs are spatially nearly homogeneous and can be given any direction and strength, up to some maximum strength.
  • the drive and focus fields are also time- dependent. The difference between the focus field and the drive field is that the focus field varies slowly in time and may have a large amplitude, while the drive field varies rapidly and has a small amplitude. There are physical and biomedical reasons to treat these fields differently. A rapidly varying field with a large amplitude would be difficult to generate and hazardous to a patient.
  • the embodiment 10 of the MPI scanner has at least one further pair, preferably three further pairs, of parallel circular coils, again oriented along the x-, y-, and z- axes.
  • These coil pairs which are not shown in Fig. 1, serve as receive coils.
  • the magnetic field generated by a constant current flowing through one of these receive coil pairs is spatially nearly homogeneous within the field of view and parallel to the axis of the respective coil pair.
  • the receive coils are supposed to be well decoupled.
  • the time-dependent voltage induced in a receive coil is amplified and sampled by a receiver attached to this coil. More precisely, to cope with the enormous dynamic range of this signal, the receiver samples the difference between the received signal and a reference signal.
  • the transfer function of the receiver is non-zero from zero Hertz ("DC") up to the frequency where the expected signal level drops below the noise level.
  • the embodiment 10 of the MPI scanner shown in Fig. 1 has a cylindrical bore 26 along the z-axis 22, i.e. along the axis of the selection field. All coils are placed outside this bore 26.
  • the patient (or object) to be imaged is placed in the bore 26 such that the patient's volume of interest - that volume of the patient (or object) that shall be imaged - is enclosed by the scanner's field of view 28 - that volume of the scanner whose contents the scanner can image.
  • the patient (or object) is, for instance, placed on a patient table.
  • the field of view 28 is a geometrically simple, isocentric volume in the interior of the bore 26, such as a cube, a ball, or a cylinder.
  • a cubical field of view 28 is illustrated in Fig. 1.
  • the size of the first sub-zone 52 is dependent on the strength of the gradient of the magnetic selection field and on the field strength of the magnetic field required for saturation, which in turn depends on the magnetic particles.
  • the first sub-zone 52 in which the magnetization of the particles is not saturated has dimensions of about 1 mm (in the given space direction).
  • the patient's volume of interest is supposed to contain magnetic nanoparticles.
  • the magnetic particles Prior to the diagnostic imaging of, for example, a tumor, the magnetic particles are brought to the volume of interest, e.g. by means of a liquid comprising the magnetic particles which is injected into the body of the patient (object) or otherwise administered, e.g. orally, to the patient.
  • An embodiment of magnetic particles comprises, for example, a spherical substrate, for example, of glass which is provided with a soft-magnetic layer which has a thickness of, for example, 5 nm and consists, for example, of an iron-nickel alloy (for example, Permalloy).
  • This layer may be covered, for example, by means of a coating layer which protects the particle against chemically and/or physically aggressive environments, e.g. acids.
  • the magnetic field strength of the magnetic selection field 50 required for the saturation of the magnetization of such particles is dependent on various parameters, e.g. the diameter of the particles, the used magnetic material for the magnetic layer and other parameters.
  • a magnetic field of approximately 800 A/m (corresponding approximately to a flux density of 1 mT) is then required, whereas in the case of a diameter of 100 ⁇ a magnetic field of 80 A/m suffices.
  • Magnetic particles that can generally be used are commercially available under the trade name Resovist.
  • the x-, y-, and z-coil pairs 12, 14, 16 generate a position- and time-dependent magnetic field, the applied field.
  • This is achieved by directing suitable currents through the field generating coils.
  • the drive and focus fields push the selection field around such that the FFP moves along a preselected FFP trajectory that traces out the volume of scanning - a superset of the field of view.
  • the applied field orientates the magnetic nanoparticles in the patient.
  • the resulting magnetization changes too, though it responds nonlinearly to the applied field.
  • the sum of the changing applied field and the changing magnetization induces a time-dependent voltage V k across the terminals of the receive coil pair along the Xk-axis.
  • the associated receiver converts this voltage to a signal S k , which it processes further.
  • the second embodiment 30 of the MPI scanner shown in Fig. 3 has three circular and mutually orthogonal coil pairs 32, 34, 36, but these coil pairs 32, 34, 36 generate the selection field and the focus field only.
  • the z- coils 36 which again generate the selection field, are filled with ferromagnetic material 37.
  • the z-axis 42 of this embodiment 30 is oriented vertically, while the x- and y-axes 38, 40 are oriented horizontally.
  • the bore 46 of the scanner is parallel to the x-axis 38 and, thus, perpendicular to the axis 42 of the selection field.
  • the drive field is generated by a solenoid (not shown) along the x-axis 38 and by pairs of saddle coils (not shown) along the two remaining axes 40, 42. These coils are wound around a tube which forms the bore.
  • the drive field coils also serve as receive coils.
  • the temporal frequency spectrum of the drive field is concentrated in a narrow band around 25 kHz (up to approximately 100 kHz).
  • the useful frequency spectrum of the received signals lies between 50 kHz and 1 MHz (eventually up to approximately 10 MHz).
  • the bore has a diameter of 120 mm.
  • the biggest cube 28 that fits into the bore 46 has an edge length of 120 mm/ ⁇ 84 mm.
  • permanent magnets (not shown) can be used. In the space between two poles of such a selection field, permanent magnets (not shown) can be used. In the space between two poles of such a selection field, permanent magnets (not shown) can be used. In the space between two poles of such a selection field, permanent magnets (not shown) can be used. In the space between two poles of such a selection field, permanent magnets (not shown) can be used. In the space between two poles of such
  • the selection field can be generated by a mixture of at least one permanent magnet and at least one coil.
  • Fig. 4 shows a general block diagram of an MPI apparatus 100 according to the present invention.
  • the general principles of magnetic particle imaging explained above are valid and applicable to this embodiment as well, unless otherwise specified.
  • the embodiment of the apparatus 100 shown in Fig. 4 comprises various sets of coils for generating the desired magnetic fields. First, the coils and their functions in MPI shall be explained.
  • selection means comprising a set of selection field coils 116, preferably comprising at least one pair of coil elements.
  • the selection means further comprises a selection field signal generator unit 110.
  • a separate generator subunit is provided for each coil element (or each pair of coil elements) of the set 116 of selection field coils.
  • Said selection field signal generator unit 110 comprises a controllable selection field current source 112 (generally including an amplifier) and a filter unit 114 which provide the respective section field coil element with the selection field current to individually set the gradient strength of the selection field.
  • the filter unit 114 can also be omitted.
  • a constant current is provided.
  • the selection field signal generator unit 110 can be controlled by a control unit 150, which preferably controls the selection field current generation 110 such that the sum of the field strength and the sum of the gradient strength of all spatial fractions of the selection field is maintained at a predefined level.
  • the control unit 150 can also be provided with control instructions by a user according to the desired application of the MPI apparatus, which, however, is preferably omitted according to the present invention.
  • the apparatus 100 further comprises focus means comprising a set of focus field coils, preferably comprising three pairs 126a, 126b, 126c of oppositely arranged focus field coil elements.
  • Said magnetic focus field is generally used for changing the position in space of the first and second sub-zones.
  • the focus field coils are controlled by a focus field signal generator unit 120, preferably comprising a separate focus field signal generation subunit for each coil element (or at least each pair of coil elements) of said set of focus field coils.
  • Said focus field signal generator unit 120 comprises a focus field current source 122 (preferably comprising a current amplifier) and a filter unit 124 for providing a focus field current to the respective coil of said subset of coils 126a, 126b, 126c which shall be used for generating the magnetic focus field.
  • the focus field current unit 120 is also controlled by the control unit 150.
  • the filter unit 124 may also be omitted.
  • the apparatus 100 further comprises drive means comprising a subset of drive field coils, preferably comprising three pairs 136a, 136b, 136c of oppositely arranged drive field coil elements.
  • the drive field coils are controlled by a drive field signal generator unit 130, preferably comprising a separate drive field signal generation subunit for each coil element (or at least each pair of coil elements) of said set of drive field coils.
  • Said drive field signal generator unit 130 comprises a drive field current source 132 (preferably including a current amplifier) and a filter unit 134 (which may also be omitted with the present invention) for providing a drive field current to the respective drive field coil.
  • the drive field current source 132 is adapted for generating a time- dependent current and is also controlled by the control unit 150.
  • detection receiving means 148 for the detection of the signals, detection receiving means 148, in particular a receiving coil, and a signal receiving unit 140, which receives signals detected by said receiving means 148, are provided.
  • detection receiving means 148 in particular a receiving coil
  • signal receiving unit 140 which receives signals detected by said receiving means 148.
  • three receiving coils 148 and three receiving units 140 - one per receiving coil - are provided in practice, but more than three receiving coils and receiving units can be also used, in which case the acquired detection signals are not 3-dimensional but K-dimensional, with K being the number of receiving coils.
  • a differential signal D k is obtained by a subtraction unit 142, which subtracts the approximation detection signals S k from the actual detection signals S k obtained by the receiving coil 148 connected to the k-th receiving unit 140.
  • the approximation detection signals S k are generally stored in digital form in an approximation detection signal storage unit 160. Details of how the approximation detection signals S k are obtained, will be explained below.
  • the obtained differential signal D k is then converted into a digital signal by the analog-to-digital converter 144 and stored in a storage unit 162. Alternatively, the differential signal D k may be stored directly in a reconstruction unit 152.
  • another differential signal D k ° is obtained as the difference between the approximation detection signal S k and the calibration detection signal S k °.
  • the calibration detection signal S k ° is obtained by the signal receiving coil 148 with an empty scanner, i.e. without magnetic particles contained in the field of view.
  • This differential signal D k ° is also converted into a digital signal by the analog-to-digital converter 144 and stored in the storage unit 162.
  • the differential signal D k ° may be stored directly in the reconstruction unit 152.
  • D k and D k ° separate subtraction units and separate analog-to-digital converters can be used, differently from the embodiment shown in Fig. 4.
  • a separate subtraction unit for subtracting the differential signal D k ° from the differential signal D k may be provided.
  • the reconstruction unit 152 which reconstructs the spatial distribution of the magnetic particles from these signals and the respective position which the first part-region 52 of the first magnetic field in the field of view assumed during receipt of the respective signal and which the reconstruction unit 152 obtains from the control unit 150.
  • the reconstructed spatial distribution of the magnetic particles is finally transmitted via the control means 150 to a computer 154, which displays it on a monitor 156.
  • a computer 154 which displays it on a monitor 156.
  • an image can be displayed showing the distribution of magnetic particles in the field of view of the MPI scanner.
  • an input unit 158 may be provided, for example a keyboard. A user is therefore able to choose the scan protocol and to set other parameters.
  • the reconstruction unit 152 (i.e. the reconstruction means) for reconstructing a concentration image of said field of view from corrected detection signals is adapted for determining said corrected detection signals from i) actual detection signals acquired at different positions of the first sub-zone with the magnetic particles arranged in the field of view, ii) calibration detection signals acquired at different positions of the first sub-zone with no magnetic particles arranged in the field of view, and iii) approximation detection signals determined as an approximation to said calibration detection signals, wherein said corrected detection signals are obtained by subtracting the difference between said calibration detection signals and said approximation detection signals from the difference between said actual detection signals and said approximation detection signals.
  • V k ° and Vk are the voltages induced by H and by M, respectively.
  • the magnetization-induced voltages are related with the acquired signals. This relationship can be written as
  • time-dependent and known function bk is the impulse response of the receiver associated with the receive coil along the Xk-axis
  • unknown constant k is proportional to the gain of this receiver.
  • the signals thus obtained are induced not by the total field H, but by the applied field H 0 . However, the difference between H and H 0 is negligible.
  • the wanted signal Sk is then found by subtracting S k ° from S k ,
  • the wanted signal (corrected detection signal) is the difference of the difference signals:
  • Suitable signals S k can be predetermined by measurement or by simulation.
  • the digital version of S k is obtained by a separate (external) processing unit or by the reconstruction unit 152.
  • the Biot-Savart law describing the magnetic field generated by an electric current may be used.
  • the digital versions of S k are obtained by m-bit AD conversion of the analog calibration detection signals S k °, e.g. by use of an m-bit AD converter.
  • This can be also be done by the apparatus shown in Fig. 4, namely by measuring signals without any object (patient) being placed in the field of view and having the subtraction unit 142 subtract nothing from the measured signals. In this way the dynamic range of the difference signal is reduced by m bits.
  • the conventionally used high-pass filtering of the received detection signals can be omitted, leading to a more complete set of received signals and a better reconstruction of images since no signal portions are lost due to filtering.
  • an explicit mathematical model of the data acquisition of Magnetic Particle Imaging is derived.
  • This model is an integral operator whose kernel can be expressed in terms of the various magnetic fields generated by the MPI scanner, the magnetization curve of the magnetic particles, the sensitivity patterns of the receive coils, and the impulse responses of the receivers. Once these ingredients have been measured or determined otherwise, the kernel is known.
  • the model is closely related to a convolution operator. This fact makes it possible to discuss the solvability of the reconstruction problem and also paves the way for fast reconstruction algorithms based on uniform and nonuniform fast Fourier trans- forms. Several such reconstruction algorithms are outlined. To make the reconstruction problem well solvable, the MPI scanner should have certain physical/technical properties. These properties are pointed out.
  • V field of view contains magnetic nanoparticles
  • H(x, t) total magnetic held, sum of selection, drive, and focus fields e( ' H) unit vector along the direction of H
  • H*(x, y) the magnetic held defined by H*(x. y) H s (x) + C(x)I*(y)
  • Magnetic Particle Imaging is an emerging medical imaging modality under development at Philips Research Europe.
  • the first versions of MPI were two- dimensional in that they produced two-dimensional images.
  • Future versions, including the Preclinical Demonstrator (PCD) under construction at Philips Research Europe, will be three-dimensional (3D).
  • PCD Preclinical Demonstrator
  • a time-dependent, or 4D, image of a non-static object can be created by combining a temporal sequence of 3D images to a movie, provided the object does not significantly change during the acquisition of the data for a single 3D image.
  • MPI is a reconstructive imaging method, like Computed Tomography (CT) or Magnetic Resonance Imaging (MRI). Accordingly, an MP image of an object's volume of interest is generated in two steps.
  • the first step referred to as data acquisition, is performed using an MPI scanner.
  • the MPI scanner has means to generate a static magnetic gradient field, the selection field, which has a single field free point (FFP) at the isocenter of the scanner.
  • the scanner has means to generate a time-dependent, spatially nearly homogeneous magnetic field. Actually, this field is obtained by superposing a rapidly changing field with a small amplitude, the drive field, and a slowly varying field with a large amplitude, the focus field.
  • the FFP may be moved along a predetermined FFP trajectory throughout a volume of scanning around the isocenter.
  • the scanner also has an arrangement of three receive coils and can record any voltages induced in these coils.
  • the object to be imaged is placed in the scanner such that the object's volume of interest is enclosed by the scanner's field of view, which is a subset of the volume of scanning.
  • the object must contain magnetic nanoparticles; if the object is an animal or a patient, a contrast agent containing such particles is administered to the animal or patient prior to the scan.
  • the MPI scanner steers the FFP along a deliberately chosen trajectory that traces out the volume of scanning, or at least the field of view.
  • the magnetic nanoparticles within the object experience a changing magnetic field and respond by changing their magnetization.
  • the changing magnetization of the nanoparticles induces a time dependent voltage in each of the receive coils.
  • This voltage is sampled and recorded by a receiver associated with the receive coil.
  • the set of the three sampled and recorded voltages constitutes the acquired data.
  • the parameters that control the details of the data acquisition make up the scan protocol.
  • image reconstruction the image is computed, or reconstructed, from the data acquired in the first step.
  • the image is a discrete 3D array of data that represents a sampled approximation to the position-dependent concentration of the magnetic nanoparticles in the field of view.
  • the reconstruction is performed by a computer, which executes a suitable computer program.
  • Computer and computer program realize a reconstruction algorithm.
  • the reconstruction algorithm is based on a mathematical model of the data acquisition. As with any reconstructive imaging method, this model can be formulated as an integral operator that acts on the acquired data; the reconstruction algorithm tries to undo, to the extent possible, the action of the model.
  • the data acquisition of MPI is afflicted by a complication: Not only the magnetization of the nanoparticles induces a voltage in the receive coils, but also the applied magnetic field itself. The receive coils pick up the sum of both voltages.
  • this wanted signal may be obtained as follows: In a separate data acquisition step, we acquire the signal generated by an empty MPI scanner, which is the signal induced by the applied field. This needs to be done only once for each MPI scanner and scan protocol. Subtracting this separately acquired signal (empty MPI scanner) from the signal at hand (non-empty MPI scanner) leaves the signal induced by the magnetized nanoparticles alone.
  • the PCD pursues a different approach and removes the unwanted signal induced by the applied field from the signal at hand by means of a high-pass filter. This is possible, because the unwanted signal is narrowly band-limited.
  • the high-pass filter also removes the lower part of the spectrum of the wanted signal and, thus, discards certain information about the concentration of the nanoparticles.
  • Such an explicit mathematical model is derived herein. This is done in two steps.
  • the first step is to derive an explicit expression for the system function in the generic model (1) in terms of the various magnetic fields produced by the MPI scanner, the magnetization curve of the magnetic nanoparticles, the sensitivity patterns of the receive coils, and the impulse responses of the receivers; once these ingredients have been measured or determined otherwise, the system function is known, up to an inessential scaling factor.
  • the second step is to relate the explicit generic model derived in the first step with an appropriate integral operator that maps functions defined in the spatial domain and representing particle concentrations onto functions also defined in the spatial domain. We shall see that this operator, M , operates according to the formula
  • the kt component of the vector—(Mc) (p(t)) represents the magnetic flux through the kth receive coil when the FFP is at p(f ).
  • the situation just described is reminiscent of MRI:
  • the data acquisition of 3D MRI has an explicit mathematical model, namely the 3D spatial Fourier transform, .
  • the data acquisition of 3D MRI provides a sampled version of the complex-valued function !Fm, where the complex- valued function m represents the transverse magnetization of the object being scanned and the samples are taken along a trajectory in 3D Fourier space that can be derived from the magnetic fields generated by the MRI scanner and from the MRI scan protocol.
  • the action of the operator ⁇ is completely different from that of the operator M, reflecting a radical difference between the imaging principles of MRI and MPI.
  • Vectors are written as column vectors.
  • the Euclidean norm of a vector a is denoted by
  • the field of view is represented by a centered subset V C IR 3 with a simple geometric shape, such as a cube, ball, or cylinder.
  • the volume of scanning is also described by a centered subset W C M 3 with a simple geometric shape.
  • Data are acquired during the time interval [i s , t e ].
  • V x H V x H (8)
  • p and j are the densities of the free charges and currents
  • D, E, B, and H are the electric flux density, electric field, magnetic flux density, and magnetic field, respectively.
  • the first of these equations plays no role in the derivation of the model. Inside the MPI scanner, the fourth equation reduces to
  • medium refers to the physical matter inside the MPI scanner during the data acquisition; of this matter, only the magnetic nanoparticles matter in MPI.
  • H 0 and H are different.
  • An analogous consideration shows that the magnetic flux density B 0 in an empty scanner is also different from the magnetic flux density B in a non-empty scanner.
  • a field like H 0 or B 0 is called an "applied field.”
  • a magnetizable medium distorts the applied field.
  • MP1 the distortion is so small that it can be safely neglected. (Including this effect in the model would make it nonlinear.)
  • a constant current I] that flows through an electromagnetic coil generates a position dependent magnetic field
  • the normalized field Hi/Ii depends only on the coil and is called the field pattern of this coil.
  • the field pattern can be computed using the Biot-Savart law.
  • a time dependent current that flows through the same coil generates the magnetic field H 1 /// 1 .
  • the field pattern is defined as ⁇ / 1 ⁇ .
  • the field pattern of a receive coil is called the sensitivity pattern of this coil.
  • the selection field may be written as
  • H s (r, ,z) ( ⁇ ?( ⁇ , ⁇ , ⁇ ). ⁇ *( ⁇ . ⁇ , (16)
  • the selection field is rotationally symmetric about the z-axis, its angular component ⁇ is zero, and the two remaining components do not depend on ⁇ .
  • the Cartesian and cylindrical components of the selection field are related by
  • H ⁇ r, z) --rG, 0 ⁇ r ⁇ r 0 , z min ⁇ z ⁇ z m;]x . (24)
  • H s (x) G ( - 3 ⁇ 4 , - ⁇ , z) ⁇ , V 2 + V 2 ⁇ r 0 , z min ⁇ z ⁇ z max . (25)
  • the (rotationally symmetric) selection field is linear in x in the region where the z-component is linear in z and independent of r. If (22) holds approximately, (25) will still hold approximately. We assume that (25) holds at least approximately in the volume of scanning, W .
  • the field pattern Cjt(x) is in V well approximated by Cfrtk for some constant c3 ⁇ 4.
  • the field matrix C(x) is nearly independent of x G V, diagonally dominant, and certainly invertible.
  • the drive and focus fields of the PCD are spatially still modestly homogeneous in V.
  • the matrices C D (x) and C F (x) are diagonally dominant and certainly invertible.
  • the fact that the drive and focus fields of the iCD have identical field matrices is exploited in the derivation of the model in Section 3.
  • the sameness of the field matrices is a consequence of the fact that the iCD, unlike the PCD, has joint coils for the drive and focus fields. If desired, (nearly) identical field matrices within the volume of scanning could also be achieved using disjoint coils.
  • the total magnetic field H(x, t) inside the MPI scanner is the sum of the static selection field and the position and time dependent drive and focus fields,
  • H(x, i) H s (x) + H D (x, + H F (x, i).
  • the total field has precisely one FFP, namely the isocenter. Adding the drive and focus fields shifts the FFP to a different position in the volume of scanning, W.
  • drive and focus fields change with time, and the FFP travels along a trajectory p : [f s , t c ] ⁇ W.
  • This FFP trajectory is implicitly defined by the equation
  • the FFP trajectory should be chosen such that it "densely' fills the volume of scanning W, or at least the field of view V C W.
  • the FFP trajectory must also be realizable by the MPI scanner at hand.
  • the drive and focus fields are added to the selection field by mak ing the currents I and ⁇ flow through the appropriate coil pairs.
  • Two problems pose themselves: First, we may want to move the FFP along a desired trajectory p : [f s , i e ] ⁇ W and need to find the currents I and / that do the job. Second, we may be given the currents and need to determine the resulting FFP trajectory. In both cases, we know the selection field and the field patterns of the coils. The first problem is solved by choosing the currents such that (38) is satisfied. To solve the second problem, we need to find, for each t e [ s , t e ], the point p(?) that satisfies H(p(i), t) 0. We work out the details for the iCD. Inserting (30) and (34) into (38) shows that the sum of the currents,
  • (40) becomes a linear system of equations for I(r). For each /, this system has a unique solution, which can be easily computed by any linear equa- tion solver. How to split up this solution into I D (0 and I F (0 is left to the designer of the scan protocol.
  • the MPI scanner must be able to realize the chosen currents. When the MPI scanner is driven with the chosen currents, eddy currents in the coils and cross coupling between the coils may cause the actual trajectory to deviate a little from the prescribed trajectory. Conversely, if 1(0 is given, (40) constitutes a (generally) nonlinear equation for p(i ).
  • I*(x) is the vector of the currents that, when flowing through the drive and focus field coil pairs (in addition to the current dz/ s that flows through the z ⁇ - coil), push the FFP from the isocenter to the point x.
  • the I* in (41) is a reparameterization and extension of the I in (40). Indeed, as can be seen from (40) and (41), we have
  • a commensurate density in 3 -direction is obtained by setting n — 84.
  • the FFP trajectory fills a cuboid of size 32 mm by 32 mm by 84 mm.
  • Preliminary considerations in Section 3 suggest that the density of the trajectory should afford a spatial resolution of the order of 1 mm in this cuboid.
  • the total duration T would increase accordingly, and the drive field would create its Lissajous curve all the time, or at least during the solid (non-dashed) portions of the meandering path in Figure 6.
  • V ⁇ and Vk are the voltages induced by H and by M, respectively.
  • M(x, f ) ni
  • L (w) behaves like coth(w), which asymptotically approaches 1.
  • of the magnetic field increases, the strength
  • an "effective" magnetization curve This curve can be measured and, like the theoretical magnetization curve (54), it will start with a finite slope and asymptotically approach a constant.
  • ⁇ t ) (v 1 (t), v 2 (t ), v 3 (t)) T (60) is the vector of the magnetization-induced voltages and
  • R(x) (R 1 (x), R 2 (x), R 3 (x)) (61 ) the sensitivity matrix of the receive coils.
  • the sensitivity matrix R(x) is nearly independent of x, diagonally dominant, and certainly invertible.
  • the signals S / ⁇ and S have an enormous dynamic range and ordinary A/D converters cannot sample these signals with the required accuracy.
  • Suitable signals S£ can be predetermined by measurement or simulation. Sampled versions of these signals can be stored in the receivers, and analog versions can be generated by D/A conversion of the sampled versions.
  • the PCD acquires the signals (cf. (64))
  • Equations (73)-(75) constitute an explicit mathematical model of the data acquisition of MPI.
  • this formulation of the model makes it difficult to answer questions such as how well the acquired signal vector s determines the wanted concentration c and how one can compute this concentration efficiently.
  • the gist of the desired transition from (73) to (76) is how to relate the spatial variable y with the time variable t .
  • such a relationship is provided by the FFP trajectory, which maps t to p(f). So we would like to reformulate (73) such that the right-hand side depends on t only via p(i). To make this possible, we need to get rid of the convolution with /3 ⁇ 4 in (74) and of the time derivative in (75).
  • H*(x,y) H s (x) + C(x)I*( ), xe ye W. (87)
  • H*(x, y) is the total field at x when the FFP is at y.
  • H*(x, y) is an extension and reparameterization of H(x, t). Indeed, comparing (87) with (44) we find that
  • H(x, t) H*(x, p(r)), x £ V, t £ [i s , t s ]. (88)
  • (Mf)(y) represents the vector of the magnetic fluxes through the three coil pairs caused by the concentration / of nanoparticles when the FFP is at y.
  • (Mf)(y) represents the vector of the magnetic fluxes through the three coil pairs caused by the concentration / of nanoparticles when the FFP is at y.
  • the second term on the right-hand-side of (93) is an unknown "constant" vector that depends on c* and p(i s ), but not on t.
  • X G 3 , (99) is also a convolution operator.
  • the operator M defined in (92) is closely related to a convolution operator.
  • the inhomogeneity term (C(x)— C(y))l*(y) comes from the spatial inhomogeneity of the drive and focus fields. This term is small to a high order of
  • ⁇ ( ⁇ ) (M 2 c*) (p(t)) - (M 2 c*) (p(t s )) + € ⁇ t ), t e [t s , t e ] , ( 104) where € ⁇ t) is a very small error term that accounts for the difference between M and M 2 .
  • mapping x h- H s (x) as a coordinate transfonnation and transform the right-hand-side of (103) using the transformation rule for multiple integrals.
  • the result reads
  • the Fourier transform of a function / may be approximated by a discrete Fourier transform (DFT):
  • iDFT inverse discrete Fourier transform
  • 1 is a set of suitable weights.
  • the accuracy of the approximation (128) depends on the sampling conditions and on the chosen weights. Direct evaluation of (128) can be computationally slow.
  • NFFT Nonuniform Fast Fourier Transform
  • a U2U-FFT/iFFT may or may not be replaced by a classical FFT/iFFT.
  • FFTs and NFFTs may be used for the following tasks:
  • Nonuniform input grid and uniform output grid Solved by density compensation plus NU2U-FFT/iFFT. This combination is also known as gridding.
  • density compensation refers to the choice of the weights in (126) or (127).
  • the gridding method is widely used for image reconstruction in MRI [4].
  • NU2U- and U2NU-FFTs/iFFTs have also been be used for other reconstraction problems [2].
  • M 4 f determines M 4 f , which determines , which determines .
  • Fourier transform theory may also be invoked to reason about the answer to the second of the above three questions. For example, the quicker the Fourier trans- formed kernel k(£ ) decays as ⁇ - 00, the more ill-posed the reconstruction problem is and the less resolution we will get. Also, from the definition of the kernel k and the shape of the magnetization curve P we can conclude that the steeper the slope of P , the slower the decay of k(£) as
  • the voxel size of the reconstructed image should reflect the achievable resolution and thus be adapted to the steepness of the slope of the magnetization curve.
  • the temporal high-pass-filtering of the received signals is not exactly equivalent to a spatial high-pass filtering of g. Nevertheless, we can try to solve an equation like
  • a simple iterative method for solving a system like (139) is the Landweber method [5 J.
  • the iterative step of this method reads u u - ⁇ ( ⁇ - A 0 ) ; ((A - A 0 )u - d), (142) where ⁇ > 0 is a relaxation parameter.
  • the bulk of the work of each iterative step of the Landweber method consists in computing matrix- vector products of the form Ap with p e K ⁇ M and A r q with q e R 3xL . Regularization may be achieved by early termination of the iteration [5]. Even so, the Landweber method is notorious for its slow convergence.
  • the matrix B is symmetric and positive definite. This makes it possible to solve (144) iteratively with the well proven linear conjugate gradient method [5]. Here is a pseudocode formulation of this method as applied to (144).
  • Minimizing a functional like (147) is a frequently seen alternative formulation of the Tikhonov-Phillips reg- ularization technique.
  • Generalizations arise when the penalty term a
  • the resulting generalized functional s may be minimized using the linear conjugate gradient method or some variant of the nonlinear conjugate gradient method [5J. In either case and once again, the bulk of the computational work is computing matrix-vector products of the form Ap and A T q.
  • [ , t & ] ⁇ is the FFP trajectory.
  • An explicit representation of the kernel of M follows from the explicit representation the system function.
  • the operator M is almost a convolution operator. Several convolution operators that approximate M well have been exhibited.
  • PCD Preclinical Demostrator

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Abstract

L'invention concerne un appareil et un procédé pour former une image de la concentration de particules magnétiques situées dans un champ de vue (28), notamment en appliquant les principes d'imagerie de particules magnétiques (MPI). L'appareil comprend un moyen de reconstruction (152) pour reconstruire une image de concentration dudit champ de vue (28) à partir d'un signal de détection corrigé (sk), lequel moyen de reconstruction (152) est conçu pour déterminer lesdits signaux de détection corrigés (sk *) à partir i) des signaux de détection réels (sk) acquis en différentes positions de la première sous-zone (301) lorsque les particules magnétiques sont disposées dans le champ de vue (28), ii) des signaux de détection de calibrage (Sk 0) acquis en différentes positions de la première sous-zone (52) sans particules magnétiques dans le champ de vue (28), et (iii) des signaux de détection d'approximation (Sk *) déterminés sous forme d'une approximation desdits signaux de détection de calibrage (Sk 0), lesdits signaux de détection corrigés étant obtenus en soustrayant la différence (Dk) entre lesdits signaux de détection de calibrage (Sk) et lesdits signaux de détection d'approximation (Sk *) de la différence (Dk) entre lesdits signaux de détection réels (Sk) et lesdits signaux de détection d'approximation (Sk *).
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CN113534025A (zh) * 2021-07-21 2021-10-22 北京航空航天大学 基于非理想无磁场点的磁纳米粒子成像方法
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US9903837B2 (en) 2011-12-15 2018-02-27 Koninklijke Philips N.V. Removal of background in MPI
EP2790574B1 (fr) * 2011-12-15 2018-03-21 Koninklijke Philips N.V. Retrait de l'arrière-plan dans mpi
JP2015531292A (ja) * 2012-10-12 2015-11-02 コーニンクレッカ フィリップス エヌ ヴェＫｏｎｉｎｋｌｉｊｋｅ Ｐｈｉｌｉｐｓ Ｎ．Ｖ． Ｍｐｉにおける動的バックグラウンド補正
US9498149B2 (en) 2012-10-12 2016-11-22 Koninklijke Philips N.V. Dynamic background correction in MPI
CN113534025A (zh) * 2021-07-21 2021-10-22 北京航空航天大学 基于非理想无磁场点的磁纳米粒子成像方法
US11454681B1 (en) * 2022-06-06 2022-09-27 Beijing University Of Aeronautics And Astronautics Magnetic particle imaging method based on non-ideal field free point

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