FIELD OF THE INVENTION

The present invention relates to an apparatus and a method for detecting and/or locating magnetic particles 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.

BACKGROUND OF THE INVENTION

Magnetic Particle Imaging (MPI) is an emerging medical imaging modality. The first versions of MPI were two-dimensional in that they produced two-dimensional images. Newer versions are 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 (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, 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. In addition, 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, called the "drive field", and a slowly varying field with a large amplitude, called the "focus field". By adding the time-dependent drive and focus fields to the static selection 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. For the data acquisition, 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 (FOV), which is a subset of the volume of scanning.

The object must contain magnetic nanoparticles (also referred to as "magnetic particles" or "nanoparticles" hereinafter); 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. During the data acquisition, the MPI scanner moves the FFP along a deliberately chosen trajectory that traces out / covers 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".

In the second step of the image generation, referred to as 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 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),

"Tomographic imaging using the nonlinear response of magnetic particles" in Nature, vol. 435, pp. 1214-1217, in which also the reconstruction principle is generally described. The apparatus and method for magnetic particle imaging (MPI) described in that publication take advantage of the non-linear magnetization curve of small magnetic particles.

Thus, magnetic particle imaging relies on the magnetic property of magnetic (nano-)particles. Typically, their response to the magnetic field is recorded a priori for a small sample, either in system calibration unit or in the MPI scanner itself when acquiring the system function. The knowledge of the system function, which contains both information about the properties of the MPI scanner (generally, the imaging device) and about the properties of the magnetic particles, is necessary for reconstruction.

SUMMARY OF THE INVENTION

It is an object of the present invention to provide an apparatus and a method for detecting and/or locating magnetic particles in a field of view which enable new applications.

In a first aspect of the present invention an apparatus for detecting and/or locating magnetic particles in a field of view is presented comprising:

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 particles 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 in the position in space of the first and second sub-zone,

storage means for storing system function data of said at least two different types of magnetic particles, said system function data describing the relation between spatial position of the respective magnetic particles and the system response for said apparatus, and processing means processing said detection signals by use of the stored system function data to obtain information about at least one type of magnetic particles in the field of view, in particular information about the spatial distribution of the at least one type of particles in the field of view.

In a further aspect of the present invention a corresponding method is presented.

In still a further aspect of the present invention a computer program comprising program code means for causing a computer to control the claimed apparatus to carry out the steps of the claimed method when said computer program is carried out on the computer is presented.

Preferred embodiments of the invention are defined in the dependent claims. It shall be understood that the claimed method and the claimed computer program have similar and/or identical preferred embodiments as the claimed apparatus and as defined in the dependent claims.

So far, magnetic particles, such as Resovist, come as a distribution of particles of different properties. In simple modeling terms, Langevin-theory could be applied and the particle diameter could be used as one key parameter. Even if monodisperse solutions of magnetic particles could be manufactured, it was so far considered impossible to discrimately reconstruct the concentration of them.

However, more parameters exist, such as anisotropy, which can lead to hysteresis. In the temporal response, this appears like a time-delay. In frequency terms, it is a frequency-dependent phase shift. The spectral response therefore becomes complex, and more data is available. Thus, for instance, magnetic particles of different hysteresis (but e.g. of identical diameters) can be separated in reconstruction.

Hence, the present invention is based on the idea to apply, preferably simultaneously, at least two different types of magnetic particles in the field of view, which can then be distinguished during the processing of the detection signals, e.g. during reconstruction from the detection signals, based on respective system function data for said types of magnetic particles, which have been previously acquired and stored in the apparatus for used during reconstruction.

Hence, various applications can be realized with the present invention. In particular, it is generally possible to obtain information about at least one type (preferably, about at least two types) of magnetic particles in the field of view. For instance, one or two images can be reconstructed from the same detection signals, said images showing e.g.

different details, different tissue or different organs. In another application, it is possible to obtain information about at least one type of magnetic particles in the field of view and/or to influence another type of magnetic particles. For instance, information about the spatial distribution of one type of magnetic particles is reconstructed or information about the surrounding tissue (e.g. its temperature) is obtained. In addition or alternatively, another type of magnetic particles can be influenced by the generated magnetic fields, e.g. can be moved through the field of view or can be heated. According to the present invention the magnetic gradient field (i.e. the magnetic selection field) is generated with a spatial distribution of the magnetic field strength such that the field of view comprises a first sub-area with lower magnetic field strength (e.g. the FFP), the lower magnetic field strength being adapted such that the magnetization of the magnetic particles located in the first sub-area is not saturated, and a second sub-area with a higher magnetic field strength, the higher magnetic field strength being adapted such that the magnetization of the magnetic particles located in the second sub-area is saturated. Due to the non-linearity of the magnetization characteristic curve of the magnetic particles the magnetization and thereby the magnetic field generated by the magnetic particles shows higher harmonics, which, for example, can be detected by a detection coil. The evaluated signals (the higher harmonics of the signals) contain information about the spatial distribution of the magnetic particles, which again can be used e.g. for medical imaging, for the visualization of the spatial distribution of the magnetic particles and/or for other applications.

Thus, the apparatus and the method according to the present invention are based on a new physical principle (i.e. the principle referred to as MPI) that is different from other known conventional medical imaging techniques, as for example local magnetic resonance (LMR) or nuclear magnetic resonance (NMR). In particular, this new MPI- principle, does, in contrast to LMR and NMR, not exploit the influence of the material on the magnetic resonance characteristics of protons, but rather directly detects the magnetization of the magnetic material by exploiting the non-linearity of the magnetization characteristic curve. In particular, the MPI-technique exploits the higher harmonics of the generated magnetic signals which result from the non-linearity of the magnetization characteristic curve in the area where the magnetization changes from the non-saturated to the saturated state.

According to a preferred embodiment said processing means comprises reconstruction means for reconstructing the spatial distribution of at least one of said at least two different types of magnetic particles, in particular of all different types of magnetic particles, in the field of view from the detection signals and the stored system function data for the different types of magnetic particles, in particular by using a combined system function data in a reconstruction algorithm.

According to another preferred embodiment said reconstruction means is adapted for reconstructing the spatial distribution of the different types of magnetic particles in the field of view from the detection signals and the stored system function data for the different types of magnetic particles being simultaneously present in the field of view by using an augmented system function being formed by combination of system function data of said different types of magnetic particles. In this way it is possible to generate an image of only the first type particles (which are e.g. in the coating of an instrument to show the instrument) and another image of only the second type particles (which are e.g. in the blood to show the vessels), despite both types are simultaneously present in the FOV.

Various embodiments exists how the magnetic particles can be designed or selected to be sufficiently different to allow discrimination. In particular, in an embodiment said different types of magnetic particles are selected to have different response in the frequency domain to an excitation, in particular have a different phase over frequency behavior. In another embodiment said different types of magnetic particles are selected to have differences in the shell and magnetic core with respect to shape, anisotropy, size and surface.

In a preferred embodiment said receiving means is adapted for acquiring detection signals with a plurality of changing excursions, excursion defining the ratio between the amplitude of the magnetic drive field and the gradient of the magnetic selection field, both of which can be changed. In this way, many independent measurements are available. For instance, to provide an example, particle 1 has a hysteresis of lOmT. If a peak amplitude of 20mT is applied for the drive field, corresponding to an excursion of +/-20 mm, these particles only provide a response signal in an area from -10 mm to +10 mm. A particle 2, without hysteresis, would, however, provide a response signal in the whole area. If the excursion is changed now, e.g. from 20mT to only lOmT corresponding to +/- 10mm, no response signal would be expected from particle 1 and thus had a simpler calculation. This embodiment particularly allows obtaining independent measurements and additional information.

Similar advantages can be obtained by another embodiment, according to which said receiving means is adapted for acquiring detection signals with constant excursion, excursion defining the ratio between the amplitude of the magnetic drive field and the gradient of the magnetic selection field, while the amplitude of the magnetic drive field and the gradient of the magnetic selection field are simultaneously changed between the acquisition of detection signals.

In a further embodiment said receiving means is adapted for acquiring detection signals with a plurality of different excitation frequencies. Hence, the possibility of obtaining different response of different nanoparticles to different frequencies can be exploited to better discriminate amongst them. With the present invention a plurality of new applications become available as defined in further dependent claims and as explained in detail hereinafter.

BRIEF DESCRIPTION OF THE DRAWINGS

These and other aspects of the invention will be apparent from and elucidated with reference to the embodiment(s) described hereinafter. In the following drawings

Fig. 1 shows a first embodiment of an MPI apparatus,

Fig. 2 shows an example of the selection field pattern produced by an apparatus as shown in Fig. 1,

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 diagrams illustrating the responses of a large concentration and of smaller concentrations of magnetic particles,

Fig. 6 shows diagrams illustrating the simulated response (magnitude and phase) of various particles,

Fig. 7 shows diagrams illustrating the theoretical response (magnitude) of a mixture of particles,

Fig. 8 shows diagrams illustrating measurements of different probes using a spectrometer,

Fig. 9 shows a flow-chart illustrating an embodiment of the proposed method, Fig. 10 shows diagrams illustrating the spectra of different probes of particles, Fig. 11 shows a diagram illustrating the a priori specified concentration vector of two different particles,

Fig. 12 shows further diagrams illustrating the responses of larger (30nm) and of smaller (25nm) nanoparticles,

Fig. 13 shows diagrams illustrating the responses of three different particles to a sinusoidal excitation without offset field, and

Fig. 14 shows a further diagram illustrating the calculated (a posteriori) concentration vector of two different particles as a result of a joint reconstruction from a given concentration as shown in Fig. 11 disturbed by noise. DETAILED DESCRIPTION OF THE INVENTION

Before the details of the present invention shall be explained, basics of magnetic particle imaging shall be explained in detail with reference to Figs. 1 to 4. In particular, two embodiments of an MPI scanner for medical diagnostics will be described. An informal description of the data acquisition will also be given. The similarities and differences between the two embodiments will be pointed out.

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. In addition, 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. For example, the y-coil pair 14 is formed by the coils at the top and the bottom of the scanner. Moreover, the coil with the positive (negative) y-coordinate is called the y -coil (y -coil), and similarly for the remaining coils. When more convenient, the coordinate axes and the coils shall be labeled 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.

It should be noted here that the arrangement of the axes and the nomenclature given to the axes in this embodiment is just an example and might also be different in other embodiments. For instance, in practical embodiments the vertical axis is often considered as the z-axis rather than the y-axis as in the present embodiment. This, however, does not generally change the function and operation of the device and the effect of the present invention.

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. In a 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. In the second sub-zone 54 (i.e. in the residual part of the scanner's field of view 28 outside of the first sub-zone 52) the magnetic field strength of the selection field is sufficiently strong to keep the magnetic particles in a state of saturation.

By changing the position of the two sub-zones 52, 54 (including the field- free point) within the field of view 28 the (overall) magnetization in the field of view 28 changes. By determining the magnetization in the field of view 28 or physical parameters influenced by the magnetization, information about the spatial distribution of the magnetic particles in the field of view 28 can be obtained. In order to change the relative spatial position of the two sub-zones 52, 54 (including the field- free point) in the field of view 28, further magnetic fields, i.e. the magnetic drive field, and, if applicable, the magnetic focus field, are superposed to the selection field 50.

To generate the drive field, 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°3 through both z-coils 16. Thus, each of the three coil pairs acts as a parallel circular coil pair. Similarly, to generate the focus field, 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.

It should be noted that the z-coil pair 16 is special: It generates not only its share of the drive and focus fields, but also the selection field (of course, in other

embodiments, separate coils may be provided). The current flowing through the z ^± -coil is I°3 + I ^F ₃ ± I ^s . The current flowing through the remaining two coil pairs 12, 14 is I° _k + I ^F _k , k = 1, 2. Because of their geometry and symmetry, the three coil pairs 12, 14, 16 are well decoupled. This is wanted.

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. In particular, the selection field has a single field- free point (FFP) at the isocenter. In contrast, the

contributions to 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 potentially hazardous to a patient.

In a practical embodiment the FFP can be considered as a mathematical point, at which the magnetic field is assumed to be zero. The magnetic field strength increases with increasing distance from the FFP, wherein the increase rate might be different for different directions (depending e.g. on the particular layout of the device). As long as the magnetic field strength is below the field strength required for bringing a magnetic particles into the state of saturation, the particle actively contributes to the signal generation of the signal measured by the device; otherwise, the particles is saturated and does not generate any signal.

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. As with the coil pairs 12, 14, 16 for the drive and focus fields, 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. For the data acquisition, 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, a cylinder or an arbitrary shape. 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. For a sufficient saturation of typical magnetic particles at a magnetic field strength of 80 A/m and a gradient (in a given space direction) of the field strength of the magnetic selection field amounting to 50xl0 ³ A/m ² , 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.

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.

Generally, various ways for bringing the magnetic particles into the field of view exist. In particular, in case of a patient into whose body the magnetic particles are to be introduced, the magnetic particles can be administered by use of surgical and non-surgical methods, and there are both methods which require an expert (like a medical practitioner) and methods which do not require an expert, e.g. can be carried out by laypersons or persons of ordinary skill or the patient himself / herself. Among the surgical methods there are potentially non-risky and/or safe routine interventions, e.g. involving an invasive step like an injection of a contrast agent into a blood vessel (if such an injection is at all to be considered as a surgical method), i.e. interventions which do not require considerable professional medical expertise to be carried out and which do not involve serious health risks. Further, non-surgical methods like swallowing or inhalation can be applied.

Generally, the magnetic particles are pre-delivered or pre-administered before the actual steps of data acquisition are carried out. In embodiments, it is, however, also possible that further magnetic particles are delivered / administered into the field of view.

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.

In the case of e.g. a diameter of 10 μιη with such magnetic particles, 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 μιη a magnetic field of 80 A/m suffices. Even smaller values are obtained when a coating of a material having a lower saturation magnetization is chosen or when the thickness of the layer is reduced.

In practice, magnetic particles commercially available under the trade name Resovist (or similar magnetic particles) are often used, which have a core of magnetic material or are formed as a massive sphere and which have a diameter in the range of nanometers, e.g. 40 or 60 nm.

For further details of the generally usable magnetic particles and particle compositions, the corresponding parts of EP 1304542, WO 2004/091386, WO 2004/091390, WO 2004/091394, WO 2004/091395, WO 2004/091396, WO 2004/091397, WO

2004/091398, WO 2004/091408 are herewith referred to, which are herein incorporated by reference. In these documents more details of the MPI method in general can be found as well.

During the data acquisition, 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. In effect, 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. As the applied field changes, 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.

Like the first embodiment 10 shown in Fig. 1 , 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.

To give a few typical parameters of such an embodiment: The z-gradient of the selection field, G, has a strength of G/μο = 2.5 T/m, where μο is the vacuum permeability. The temporal frequency spectrum of the drive field is concentrated in a narrow band around 25 kHz (up to approximately 150 kHz). The useful frequency spectrum of the received signals lies between 50 kHz and 1 MHz (eventually up to approximately 15 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.

Since the construction of field generating coils is generally known in the art, e.g. from the field of magnetic resonance imaging, this subject need not be further elaborated herein.

In an alternative embodiment for the generation of the selection field, permanent magnets (not shown) can be used. In the space between two poles of such

(opposing) permanent magnets (not shown) there is formed a magnetic field which is similar to that shown in Fig. 2, that is, when the opposing poles have the same polarity. In another alternative embodiment, 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.

For generating the magnetic selection field explained above, selection means are provided 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. Preferably, 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. However, since the selection field is generally static, the filter unit 114 can also be omitted. Preferably, a constant current is provided. If the selection field coil elements are arranged as opposite coils, e.g. on opposite sides of the field of view, the selection field currents of the opposite coils are preferably oppositely oriented.

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. For this purpose 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.

For the generation of a magnetic focus field 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. With the present invention, the filter unit 124 may also be omitted.

For generating the magnetic drive field 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 be present but may also be omitted in embodiments in accordance 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. It should be noted that in the embodiment of the apparatus 10 shown in Fig. 1 identical coils are preferably used for generating the magnetic drive field and the magnetic focus field.

For signal 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. Preferably, 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.

Said signal receiving unit 140 comprises a filter unit 142 for filtering the received detection signals. The aim of this filtering is to separate measured values, which are caused by the magnetization in the examination area which is influenced by the change in position of the two part-regions (52, 54), from other, interfering signals. To this end, the filter unit 142 may be designed for example such that signals which have temporal frequencies that are smaller than the temporal frequencies with which the receiving coil 148 is operated, or smaller than twice these temporal frequencies, do not pass the filter unit 142. The signals are then transmitted via an amplifier unit 144 to an analog/digital converter 146 (ADC). The digitalized signals produced by the analog/digital converter 146 are fed to an image processing unit (in an embodiment preferably including a reconstruction means) 152, which determines (e.g. 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 examination area assumed during receipt of the respective signal and which the image processing 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. Thus, an image can be displayed showing the distribution of magnetic particles in the field of view of the examination area.

Further, an input unit 158 may be provided, for example a keyboard. A user may therefore be able to set the desired direction of the highest resolution and in turn receives the respective image of the region of action on the monitor 156. If the critical direction, in which the highest resolution is needed, deviates from the direction set first by the user, the user can still vary the direction manually in order to produce a further image with an improved imaging resolution. This resolution improvement process can also be operated automatically by the control unit 150 and the computer 154. The control unit 150 in this embodiment sets the gradient field in a first direction which is automatically estimated or set as start value by the user. The direction of the gradient field is then varied stepwise until the resolution of the thereby received images, which are compared by the computer 154, is maximal, respectively not improved anymore. The most critical direction can therefore be found respectively adapted automatically in order to receive the highest possible resolution.

According to the present invention a storage unit 160, e.g. a semiconductor memory device, is provided for storing system function data of two or more different types of magnetic particles that may be used (simultaneously or subsequently) in an MPI data acquisition. Said system function data generally describe the relation between spatial position of the respective magnetic particles and the system response for said MPI apparatus (i.e. the scanner) and have been previously acquired (e.g. at the manufacturer of the tracer materials (each containing preferably only one type of magnetic particles), at the manufacturer of the magnetic particles, at the manufacturer of the MPI apparatus, or at the user of the MPI apparatus after its installation). Methods for obtaining such system function data will be described below.

Further, the processing unit 152 is adapted according to the present invention for processing said detection signals by use of the stored system function data to obtain information about at least one type of magnetic particles in the field of view, in particular information about the spatial distribution of the at least one type of particles in the field of view. Here, the term "information" shall be understood broadly, i.e. including various kinds of information, such as information about the spatial distribution, the speed of flow, the density, the temperature, etc. Preferably, the processing unit 152 is adapted to obtain information about the spatial distribution of at least two different types of magnetic particles in the field of view or to obtain information about at least one type of magnetic particles in the field of view and to influence another type of magnetic particles.

In particular, in an embodiment the processing unit 152 comprises a reconstruction unit 152 which is adapted according to the present invention for reconstructing the spatial distribution of at least one of said at least two different types of magnetic particles in the field of view from the detection signals and the stored system function data for said at least one type of magnetic particles. For instance, an image of the field of view can be generated showing various details from detection signals originating from different types of magnetic particles present in the field of view. A plurality of applications is possible as will be explained below in detail.

So far, nanoparticles, such as Resovist, come as a distribution of particles of different properties. In simple modeling terms, Langevin-theory could be applied and the particle diameter could be used as one key parameter. Even if one could manufacture monodisperse solutions of magnetic particles, it was so far considered impossible to discrimatively reconstruct the concentration of them.

The reason is visible in Fig. 5. The curve 200 in Fig. 5 A shows the response of a large concentration of small particle in a central position (represented by the rectangle 202). The response is relatively wide allowing only weak resolution. In Fig. 5B, the curves 210, 212, 214 shows the responses of three smaller concentrations of larger particles (represented by the rectangles 216, 218, 220). They have a sharper response, allowing for higher resolution. The dashed curve 222 in Fig. 5B shows the summed response of the three concentrations. It is very similar to the response 200 shown in Fig. 5 A. Extrapolating to more locations, it is difficult or even impossible to differentiate between Langevin-particles of different diameters.

However, more parameters exist, such as anisotropy, which can lead to hysteresis. In the temporal response, this appears like a time-delay. In frequency terms, it is a frequency-dependent phase shift. The spectral response therefore becomes complex, and more data is available. In this context, magnetic particles of, e.g. different hysteresis (but e.g. of identical diameters) can be separated in reconstruction.

Fig. 6 shows the simulated response of such particles. Particle 1 (depicted as continuous line 230 in Fig. 6A showing the magnitude and 232 in Fig. 6B showing the phase) is 30nm in diameter and has no hysteresis, ff is the number of the harmonic. Particle 2 (shown as dashed line 240 in Fig. 6A and 242 in Fig. 6B) has the same diameter and hysteresis. The response is shown for a sinusoidal excitation without offset, therefore no even harmonics appear in the magnitude (but nevertheless appear as arbitrary phase).

As a proof of the existence of such different particles, the theoretical response of such a mixture of particles is shown in Fig. 7. In said mixture the particles have nearly identical concentrations and identical amplitudes over frequency response, but different phase over frequency responses. Due to destructive interference, characteristic cancellations appear at some frequencies. Measurements of certain probes in the spectrometer, as provided in Fig. 8, show the same effect, which indicates, that different particles are well present in already available (and approved) tracer materials.

A preferred embodiment of the method according to the present invention is shown in the flowchart depicted in Fig. 9. This embodiment of the method comprises the following steps: S10: Manufacturing of "orthogonal" tracers ("tracer" meaning "contrast agent" or

"magnetic particles"), e.g. having (e.g. same diameters but) different hysteresis.

S 11 : Measure the magnetic response/system function for each of them (e.g. at the site of the manufacturer of the tracer, or at the end-user site). The response can be regarded as a spectrum of the harmonics (having magnitude and phase, represented e.g. by a (complex- valued) matrix of the dimension n x m (n being the number of points in space, e.g.

16x16x16=4096) and m being the number of harmonic and mixing frequencies (e.g.

approximately 10000). Typically, the system function is obtained in the scanner using a 3D sequence. Thus, not only the respective (approximately 40) harmonics of the three slightly different basic frequencies are generated, but also a large number (thousands) of mixing frequencies. Some of them are not evaluated so that approximately 10000 mixing frequencies remain.

S12: Apply at least two "orthogonal" tracers to the imaging volume.

S 13 : Measure the MPI response.

S14: Reconstruct using a special algorithm. The unknown to be solved for is a vector of concentrations in the imaging volume, which is augmented from the standard vector by the additional unknown concentrations of a second (and possibly third etc.) magnetic particle. The system function, too, is augmented by joining the two (or three or more) separate system functions of the additional tracers (magnetic particles) (e.g. resulting in a (complex-valued) matrix of dimension (2n) x m). The reconstruction then uses generally known methods for reconstruction, e.g. a least square method, regularization, etc.

S15: Compared to a standard one-particle reconstruction, twice (or more) the number of data needs to be extracted from the same single measurement. Therefore more noise appears in the reconstructed results. In order to keep the same apparent SNR in the image, the voxel count can be decreased. Half the number of voxels per volume means an increase in voxel size in all direction by a factor of 3rd square of 2 = 1.26. If the same SNR shall be achieved for the original voxel size, then the data acquisition needs to be prolonged in order to reduce noise from the raw data.

SI 6: Alternatively, more "orthogonal" measurement data can be added in the reconstruction. Several measurements with changing excursions (= max. distance of FFP from center) can be performed, and the concentration can be derived by optimizing simultaneously to all data. This particularly allows obtaining independent measurements and additional information. Alternatively, the excursion can be kept constant, whilst changing simultaneously drive field amplitude and selection field, (excursion = ratio of DriveFieldAmplitude / SelectionFieldGradient).

It should be noted that step S12 is usually performed just at the beginning of data acquisition or even during data acquisition. There are many ways to apply

(simultaneously or subsequently) at least two "orthogonal" tracers to the imaging volume. If the imaging volume is (part of) a patient, the tracers can be administered (by the patient himself or by an administering person) orally, by injection, by inhalation, by swallowing, etc., i.e. including various non-invasive and non-surgical methods.

The tracer can also enter the imaging volume in the way together with the patient, as it might be already inside the patient, e.g. as part of an implant, stent, etc.

Furthermore, the tracer can be part of a surgical instrument, catheter etc., e.g. for the purpose of making it visible within an interventional MPI procedure. Another way of bringing the tracer into the patient is by loading it into cells, e.g. erythrozytes or macrophages, that are administered, e.g. by systemic injection or swallowing, to the patient.

Further, it should be noted that steps S10 to SI 1 are initial steps generally performed in advance and only once (e.g. at the manufacturer of the tracer material).

Methods and devices for acquiring the system function of a tracer material for use in an MPI method are generally known. For instance, WO 2010/067264 Al and WO 2010/067248 Al describe devices and method which reduce the size of the generally quite large system function matrix by making use of structural properties of the matrix. Such properties are, for instance, spatial symmetries reducing the number of columns and identical responses at different frequencies reducing the number of rows. In other embodiments the matrix can be transformed to a sparse representation using appropriate base functions. Such description about how to obtain the system function provided in those documents are herewith incorporated by reference.

Another embodiment for acquiring the system function uses a magnetic spectrometer, which is an instrument that excites a probe of e.g. magnetic nanoparticles with a pure sinusoidal magnetic field, e.g. at 25kHz. The response at many harmonics, e.g. up to 1MHz, is measured and analyzed, and serves as a "fingerprint" of the particles. The system is calibrated by introducing a miniature coil into the measurement chamber and to drive it at the harmonics.

The phenomenon termed "harmonic nulling" appears when particles with and without hysteresis (or particles with different hysteresis) are mixed and their joint spectrum is analyzed. As the phases of the harmonics are different between the two types of particles, they add up at some frequencies (constructive interference) and null out at others (destructive interference). This phenomenon is exploited in a further embodiment for obtaining the system function data, when an unknown tracer material (particle) is mixed with a known one. The known one is e.g. characterized a priori, possibly at a different site (e.g. the

manufacturer's site) by a calibrated instrument. Thereby, the precision of the calibrated instrument can be transferred to a local instrument with weaker performance. Harmonic nulling permits to indirectly measure the hysteresis of the unknown particles. Detecting a null is relatively simple compared to determining precise figures. Hence, the instrumentation is simplified as it neither requires measuring the fundamental frequency, nor calibrating at the harmonics. The instrumentation is additionally insensitive to drift and temperature effects.

The measurement can be repeated at various drive field levels and at various drive field frequencies. The mixing of the unknown can be done with several concentrations of known tracer material ("references"). In order not to waste material by mixing it (and finally dispose of it), it would be possible to have two measurement volumes (chambers) which are electrically placed in series (or parallel). Thereby, the interference will be electrically. The references will remain pure and can be used again and again.

Ample applications of the present invention can be envisaged. Besides vascular imaging, where only one type of magnetic particles is required to be present at a time, more advanced applications are foreseeable, with different magnetic particles being simultaneously present in the imaging volume. As they generate different magnetic fingerprints, it becomes necessary to be able to distinguish them within the process of image reconstruction. Such applications may be applied separately, but may also be combinations of the following ones:

Apply particle 1 to blood and let it circulate a few rounds to reach equilibrium concentration in whole blood volume. Then an orientation scan can be performed to localize the organs of interest. Then, set FOV to wherever desired, e.g. heart, and observe arrival of bolus of particle 2. Such examination would provide a kind of background image behind the actual bolus information.

Apply particle 1 to red blood cells and use particle 2 for bolus type applications.

Apply particle 1 to red blood cells and particle 2 to white blood cells.

Discriminative imaging would allow to measure the ratio of the two at a local level, permitting e.g. to localize inflammations. Just knowing where many white blood cells are located could erroneously point to areas with much blood. Apply particle 1 to blood, or blood cells, and particle 2 to instrumentation such as catheters, micro-devices (to be e.g. navigated also by MPI technology), stents, local implants, meshes for hernia repair, etc. to make them visible during MPI-guided

interventions or regularly scheduled MPI-based control examinations, or even to guide said instrumentation by the magnetic fields generated by the MPI scanner.

Apply particle 1 to blood, or blood cells (e.g. via systemic injection in advance to data acquisition), and inject particle 2 interstitially into an organ/a cancer. Possibly use particle 2 for hyperthermia application and particle 1 for general investigations, or also temperature supervision during heat ablation.

- Inject magnetic particles into one or several body liquids to visualize the vascular-, lymph-, cerebrospinal fluid- or ureter/urethra-system. This will allow to wide range of examinations, including the localization of leakage and reflux phenomena.

Magnetic particles are inhaled, swallowed, or given as an enema, for the visualization of the nose, lung, esophagus, as well as the whole range of the gastro-intestinal tract. If e.g. particle 1 is applied systemically to blood, and particle 2 to the gastro-intestinal tract, the lumen and the colon wall can both be visualized. In a healthy tract, there should be no blood in the lumen. If particle 1 and particle 2 are present in the same location/voxel, then this is only possible at the interface between lumen and colon wall. Such interface is a two- dimensional surface, basically a curved tube. If, however, both particles are present in a three-dimensional structure, then this must be due to a leakage between colon wall and lumen. Thereby, this method allows localizing the point of bleeding. Blood in stool can have various origins as is classified in hematochezia and melena. The search of the location of the blood leakage point nowadays usually requires an esophagogastroduodenoscopy, and thereafter, possibly, a coloscopy. Nevertheless, bleeding points within the small intestine cannot be localized. This will all be possible with the present invention. Magnetic particles are deliberately internalized into erythrocytes to take advantage of their long blood circulation time.

Magnetic particles are taken up by macrophages which allows localizing inflammations as well as atherosclerotic plaque formation.

In addition to the simultaneous application of various magnetic particles, different magnetic fingerprints can also originate from local interaction of the magnetic particles with their environment, on a cellular and even molecular level. Evidence of such interaction exploitable in MPI comes from various sides:

Low-frequency magnetic particle spectroscopy at 270 and 790 Hz shows that in-vitro endocytosis of magnetic particles causes pronounced changes to the magnetic fingerprint, as for instance described in A. Rauwerdink et al, Magnetization harmonics as a remote method of monitoring endocytosis of nanoparticles, Proceedings of the First

International Workshop on MPI, World Scientific Publishing, 2010, pp. 79-85. However, it was yet impossible to tell it apart from Concanavalin-A-induced aggregation of the dextran- coated magnetic particles, which has a very similar impact on the Brownian particle motion. Whilst it is possible to find concentration- independent metrics in order to quantify an effect, work is ongoing to be able to separately estimate the simultaneous influence of multiple in- vivo parameters such as binding, viscosity, temperature and aggregation. One promising path ahead is to sweep the magnetic excitation amplitude and frequency.

A change of the viscosity of the surrounding liquid modifies also the

Brownian motion and hence the magnetic fingerprint, as described for instance in the above cited article of A Rauwerdink. This effect is visible below 1kHz in experiments, in which the viscosity is deliberately tuned by altering the glycerol/water mixture. Experimental results shown in Fig. 10, where Brownian motion is completely inhibited by immobilizing the magnetic particles in gelatin, confirm this effect at 25kHz. Fig. 10 shows spectra of ΙΟμΙ samples of 10% Resovist in gelatin, excitation 25kHz, 10mT _pk . The particles maintain the orientation which has been enforced by applying a magnetic field during the 'solidification' process. Surrounded by solidified gelatin, the particles are immobilized and Brownian motion and rotation is inhibited, thereby modifying the magnetic fingerprint. The engendered harmonics of transversally oriented particles (3) are weak; also the unoriented (1) ones (no- field during solidification) are only marginally stronger. The axially magnetized MNPs (2), however, generate much stronger harmonics, comparable to mobile particles in water (5). The odd harmonics are representing the nonlinearity of the magnetization curve. The steeper the decay towards high frequencies, the less spatial resolution can be achieved with the particles. According to ideal Langevin theory, the larger the particles, the less field is required to bring them into saturation, and hence the stronger odd harmonics are generated. The even harmonics, as visible above, are from residual DC offset fields within the magnetic spectrometer set-up and irrelevant.

- Chemical binding, such as antibody binding of targeted diagnostic and therapeutic agents, also manifests itself as a modification of the low- frequency magnetic fingerprint, as described for instance in J.B. Weaver, A.M. Rauwerdink, The effects of molecular binding on the phase of MSB measurements, Proceedings of the First International Workshop on MPI, World Scientific Publishing, 2010, , pp. 19-25. However, if only the amplitudes of the harmonics are measured, the changes caused by binding cannot be distinguished from changes in nanoparticle concentrations. It can be demonstrated that chemical binding also changes the phases of the harmonics in addition to their amplitude, and that the relative phase of the 3 ^rd and 5 ^th harmonics provides a concentration independent measure of chemical binding.

Magnetorelaxometry experiments also show that bound and unbound nanoparticles can be distinguished, as described for instance in D. Rufimer et al., Magnetic relaxation imaging of magnetic nanoparticle distributions, WC2009 Munich, IFMBE proceedings, 25/VII, pp. 418-420, 2009. Binding of magnetite nanoparticles functionalized with streptavidin to surfaces (biotinylated plastic foils) immobilizes them due to the specific biotin-streptavidin binding and hence inhibits Brownian motion. The immobilized nanoparticles can only relax via the Neel mechanism, which leads to a different relaxation time constant. In this 2D-scanning experiment, it was proven that magnetorelaxometry is suitable for the detection of tiny amounts of bound magnetic particles even in the presence of larger amounts of unbound magnetic particles.

In an attempt to increase patient compliance for the early detection of colorectal cancer, MPI could be employed in the future for lesion visualization, as described for instance in K. Ramaker, N. Rockendorf, A. Frey, The lack of a mucosal glycocalyx as a potential marker for the detection of colorectal neoplasia by Magnetic Particle Imaging", Proceedings of the First International Workshop on MPI, World Scientific Publishing, 2010, p. 239. To this end, magnetic particles ought to be covered with membrane receptor ligands in order to bind selectively to neoplastic cells that lack a glycocalyx. In order to distinguish the bound particles, either their concentration must be much higher than on healthy tissue, or their magnetic fingerprint should be tailored to make them distinguishable.

- Very high local particle concentrations, as evidenced in agglomerations of particles in cells, cause particle-particle interactions that alter the magnetic fingerprint, as described for instance in J.-P. Gehrcke et al., Investigation of the MPI signal's dependency on ferrofluid concentration", Proceedings of the First International Workshop on MPI, World Scientific Publishing, 2010, pp. 73-78.

- More generally, if a particle is tailored such as that its hysteresis changes (in general that its magnetic fingerprint changes) with a parameter of the surrounding

liquid/tissue (such as temperature, pH, pressure, etc), the discriminative reconstruction allows measuring these parameters at all locations within the FOV simultaneously. One mechanism to achieve this could be to immerse the magnetic particles in a droplet, the viscosity of which is modified by the parameter of interest.

If a particle is tailored such as that its magnetic response (in amplitude) increases/weakens (whilst keeping the same phase properties) with a parameter of the surrounding liquid/tissue (such as temperature, pH, pressure, etc), the discriminative reconstruction allows measuring the changing apparent concentration of this particle 1. As the general concentration of blood/nanoparticles also needs to be known, a second particle 2 is measured to allow for normalization. One possibility of weakening magnetization could be due to nanoparticles (or the cells that are loaded by them) are being broken up by

macrophages or other mechanisms unknown to RF engineers. Another mechanism could be due to surpassing the Curie-temperature.

A ID-simulation study has been set out with two different particles being present simultaneously. Generally, the results of this study are also applicable and valid for three dimensions. 17 concentration values within the 1mm "voxels" in the range from -8mm to + 8mm are specified a priori for both particles as shown in Fig. 11. Said figure shows the a priori specified concentration vector CAB of particles A and B, i.e. concentration in arbitrary units versus position in mm. Based upon CAB, the response vector VAB is calculated, following a modified Langevin-model and with adding noise. From VAB, the original concentration vector CAB shall be reconstructed. The particles' response to the sinusoidal magnetic excitation (fo=25kHz, FOV=+/- 25mT _pk /(2.5T/m) = +/- 10mm) is calculated in the time- domain according to ideal Langevin theory that is simplistically modified by a time delay τ in order to account for hysteresis. As hysteresis is engendered by energy barriers to be overcome, such model is only a simple approximation.

Three different particles are considered. Particle A has a core diameter of 30nm and no delay. Particle Bl and B2 differ from A by a smaller core of only 25nm and a delay corresponding to a phase lag of 10°, respectively. For each particle, a 25* 17 size matrix G termed "system function" is derived containing the complex responses at frequencies 2f ₀ to 26fo = 650kHz for a normalized concentration at each of the 17 locations. For one particle type, the complex response vector v is derived via matrix- vector multiplication v = G * c, with c being the particle concentration vector. When two particles are simultaneously excited, the response becomes

VAB = G _A * CA + G _B * C _B ,

which can be rewritten as

VAB = [G _A G _B ] * [c _A ; <¾] = GAB * CAB, with G _AB having a size of 25*34 and C _AB being a vector with 34 concentrations. Finally, noise is added to the response vector V _AB - Its intensity is chosen such as to be equal to the signal strength at 650kHz. The acquisitions of the individual system functions G _A and G _B

themselves are considered noiseless. This is motivated by the higher concentrations that can be used during system function acquisition, whilst refraining from the highest concentrations that would lead to non-linear particle-particle interactions. Reconstruction, i.e. the determination of the unknown concentrations C _AB from the knowledge of a noisy response vector V _AB and the joint system function G _AB , requires to invert the matrix- vector

multiplication. As the linear equation system is over-determined, G _AB is not square, and hence a solution is calculated by regularization, with the complex response vector V _AB and the complex matrix G _AB rewritten as real quantities of size 50 and 50*34, respectively. The regularized least-square problem

\\Gc - v|| ₂ + ||c|| ₂ min

can be transformed into its normal equation:

(G ^H G + λΐ) c = G ^H v.

This square linear system is finally inverted by singular-value-decomposition:

c = (G ^H G + λί) G ^H v.

It has been found that for most applications distinguishing ideal Langevin particles A and Bl, which only differ with respect to core size, is difficult if not impossible. The reason for this is illustrated in the time domain in Fig. 12. This figure shows responses in the time-domain (arbitrary units), simulated for the field- free point (FFP) travelling across the sketched concentration at constant speed. On the left, the concentration of particles A and Bl is identical (particle A is an ideal Langevin model for 30 nm core, particle Bl is an ideal Langevin model for 25 nm core). The response of Bl, the particle with the smaller core, is distributed more widely, and has a lower peak. On the right, the response of a localized concentration of Bl is compared to a distributed concentration of A spreading over 5 positions. For an infinitely fine, i.e. not spatially discretized distribution concentration of A, the response cannot be distinguished from the response of a single local concentration of B.

Expressed in frequency domain terms, the spectra of A and Bl, both of which are purely real, are not sufficiently different. It is necessary to have different phase information within the spectrum, as is the case for the combination of particles A and B2 (particle A is an ideal Langevin model for 30 nm core showing no hysteresis, particle Bl is an ideal Langevin model for 25 nm core showing no hysteresis, particle B2 is an ideal Langevin model for 25 nm core showing 10° hysteresis). Fig. 13 shows amplitude and phase characteristics of all three investigated particles. In particular, the responses in the frequency- domain to a sinusoidal excitation without offset field are shown. Only odd harmonics are generated, and principally sketched. Particles A and Bl have a constant phase of 90°, as the induced voltage is the derivative of the magnetic response. Particle Bl has a stronger decay of the amplitude of the higher harmonics than A due to its smaller size. Particle B2 has frequency-dependent phase as it is delayed due to model hysteresis.

The reconstruction of the A/B2-combination for a regularization parameter λ=0 is shown in Fig. 14. In particular, the reconstructed concentration vector CAB of particles A and B2 is shown. The concentration is in arbitrary units versus position in mm and is reconstructed from a noise-affected response vector VAB- The calculated concentration resembles the original vector (cf. Fig. 11), and proves the distinguishability between particles even for the chosen low SNR condition. For this case, it is well possible to distinguish the particles. Reconstruction artifacts become visible, such as negative concentrations, crosstalk between particles, and smearing into neighbor locations. By better regularization and higher signal-to-noise ratio, these can be further suppressed.

Hence, in summary the combination of spatial resolution and of particle distinction within MPI has been proven. Whilst a joint reconstruction works for particles with sufficiently different magnetic fingerprints, it needs to be kept in mind that one attempts to extract more information from the same measurement. This means that, for a given signal-to- noise ratio, resolution or speed have to be sacrificed for particle distinction within MPI. As real particles will often have some effect of phase lag, there is in practice no single threshold on the MPI ability to distinguish them. It is rather dependent on the instrumentation (receiver bandwidth, noise, selection field gradient, magnetic excitation amplitude), and the chosen scanning parameters (trajectory of the field-free point, desired temporal and spatial resolution). In any case, more independent data, such as sweeps over excitation frequency and amplitude, as well as selection field gradient, will improve distinguishability, which ultimately is not limited to two particles or two in-vivo parameters. This opens up the route to many exciting medical applications.

It has particularly been recognized that the different magnetic particles that the response (i.e. the harmonics) do not only have an amplitude, but also a phase, which is a result of the non-synchronous (i.e. time displaced) response of the particles and which result in a hysteresis in response to a sinusoidal excitation, by which the different particles can be distinguished when evaluating acquired detection signals. While the invention has been illustrated and described in detail in the drawings and foregoing description, such illustration and description are to be considered illustrative or exemplary and not restrictive; the invention is not limited to the disclosed embodiments. Other variations to the disclosed embodiments can be understood and effected by those skilled in the art in practicing the claimed invention, from a study of the drawings, the disclosure, and the appended claims.

In the claims, the word "comprising" does not exclude other elements or steps, and the indefinite article "a" or "an" does not exclude a plurality. A single element or other unit may fulfill the functions of several items recited in the claims. The mere fact that certain measures are recited in mutually different dependent claims does not indicate that a combination of these measures cannot be used to advantage.

Any reference signs in the claims should not be construed as limiting the scope.