EP4673756A1

EP4673756A1 - Rotatable magnetic fields

Info

Publication number: EP4673756A1
Application number: EP24707087.3A
Authority: EP
Inventors: Gilad LIBERMAN; Torben SCHEIDER; Pedro Freire SILVA; Henrik GOTHEN
Original assignee: Deepspin GmbH
Current assignee: Deepspin GmbH
Priority date: 2023-02-28
Filing date: 2024-02-28
Publication date: 2026-01-07
Also published as: WO2024180144A1

Abstract

A method of magnetic resonance image acquisition, comprising repeatedly generating a static magnetic field that has a first direction in a field of view, a gradient magnetic field and an RF excitation field that has a second direction in the field of view, wherein the second direction is substantially perpendicular to the first direction and obtaining an NMR signal caused by the RF excitation field. At least one of the first direction and a direction of the gradient magnetic field is changed between repetitions and, when the first direction is changed, the second direction is also changed so that it remains substantially perpendicular to the first direction in each repetition.

Description

Rotatable magnetic fields

FIELD

Embodiments generally relate to low field MRI in using inhomogeneous fields. In particular, embodiments relate to coil pairs for generating rotating fields, coil pairs for generating rotationally symmetric fields, systems including one or more of such coil pairs and methods of designing coils.

BACKGROUND

Many MRI systems are rotationally symmetric around one axis. In particular, many MRI systems have a cylindrical configuration. Rotational symmetry is far harder to achieve in systems in which the static and varying magnetic fields used for MRI are generated by hardware that is not distributed around the volume of interest to be imaged but that is, instead, located on a limited number of the sides surrounding the volume of interest. Such systems are referred to as projected field systems and may be systems in which the hardware that is configured to generate the static and/or varying magnetic fields used during an MRI image acquisition are located on only one side of the volume of interest, for example below the volume of interest, for example in a patient bed.

Nuclear magnetic resonance (NMR) measures the interaction between atomic nuclei and an external magnetic field and can be used to probe materials and biological tissue in a non-invasive manner. A careful manipulation of the external magnetic field allows to estimate certain tissue properties such as total water content, tissue composition or the presence of motion such as microscopic diffusion or macroscopic flow. Furthermore, the field can be manipulated in such way to resolve these properties in space, to generate magnetic resonance images.

Conventionally, NMR and MRI for clinical human application rely on the presence of a strong, spatially homogeneous, and non-time-varying magnetic field, typically on the order of 0.5-10T. This field is referred to as B_o. In addition, these systems can also generate weaker, time-varying fields on the order of a few pT to tens of mT using Bi transmission coils and gradient coils.

Bi transmission coils generate one or more weak homogeneous fields that may have, for example, a strength of less than 1 mT and that are aligned perpendicular to the static magnetic field B_o. The Bi field can be pulsed at high frequencies to excite spins in underlying tissue.

Multiple time- and spatially-varying gradient fields are employed to resolve tissue properties in 3-dimensional space. These magnetic fields typically vary the total field amplitude linearly (1st order) or non-linearly (2nd order or higher) and are able to generate maximum of 10-100 mT/m variation over a typical Field of View (FOV) of a clinical MRI experiment.

BRIEF DESCRIPTION OF THE DRAWINGS

Fig. 1 shows a known projection type NMR system;

Fig. 2 illustrates the principles of a known imaging method;

Fig. 3A shows and example of an uncoupled pair of coils;

Fig. 3B shows and example simulation of static magnetic B_o fields generated by the individual coils of the pair of coils shown in Fig. 1A;

Fig. 4A shows radial and angular orders of stream functions;

Fig. 4B shows the magnetic field generated by the corresponding stream function of Fig. 4A when approximated by discrete wire windings;

Fig. 5A shows a B_o magnetic field generated by a coil of an embodiment;

Fig. 5B shows a gradient magnetic field generated by a coil of an embodiment;

Fig. 5C shows a combination of the fields shown in Fig. 5A and 5B;

Fig. 5D shows indicates the locations of the plots shown in Fig. 5E in the combined field shown in Fig. 5C;

Fig. 5E shows the distribution of the combined field along the lines indicated in Fig. 5D;

Fig. 5F shows an example of rotation of the field shown in Fig. 5C;

Fig. 5G shows another, different combination of the fields shown in Fig. 5A and 5B;

Fig. 5H shows an example of rotation of the field shown in Fig. 5G;

Fig. 6 shows an example of a pulse sequence that may be used with uncoupled pairs of B_o coils, gradient coils and B coils.

DETAILED DESCRIPTION

According to embodiments there is provided a method of magnetic resonance image acquisition, comprising: repeatedly: generating a static magnetic field that has a first direction in a field of view, a gradient magnetic field and an RF excitation field that has a second direction in the field of view, wherein the second direction is substantially perpendicular to the first direction; and obtaining an NMR signal caused by the RF excitation field; wherein at least one of the first direction and a direction of the gradient magnetic field is changed between repetitions; and wherein, when the first direction is changed, the second direction is also changed so that it remains substantially perpendicular to the first direction in each repetition.

In an embodiment one or more or all of the static magnetic field, the gradient magnetic field and the RF excitation field is generated using a planar coil, preferably on a PCB, more preferably on a multi-layered PCB.

In an embodiment one or more or all of the static magnetic field, the gradient magnetic field and the RF excitation field extend in a direction parallel to a plane occupied by the coil generating the respective field.

The method preferably further comprises changing the direction of the gradient magnetic field between repetitions, so that a way the gradient magnetic field modifies the static magnetic stays the same, irrespective of the first direction adopted by the static magnetic field.

The method preferably further comprises overlaying the static magnetic field with a further static magnetic field to generate a net static magnetic field that, by virtue of the changes in the first direction over the repetitions, adopts positions on a cone defined by the magic angle.

Alternatively, the coils used in generating the static magnetic field and their driving circuits may be configured to cause rotation of the net static magnetic field in a cone defined by the magic angle.

According to an embodiment there is provided pair of coils comprising a first coil and a second coil, wherein the first and second coils are configured to generate identical field distributions that are rotated relative to each other, the field distributions of the first and second coils jointly generating a net field distribution, wherein the first and second coils are independently actuable and wherein the field distributions are configured so that actuation of the coils allows the net field distribution to rotate about an axis perpendicular to the net field distribution.

Preferably the first and second field distributions are each rotationally symmetric.

In an embodiment the first and second coils are electrically insulated from each other. In an embodiment the coils generate a static magnetic B_o field. In an embodiment the coils generate a B1 RF field. In an embodiment the coils generate a gradient magnetic field.

In an embodiment the first coil and the second coil are provided in a multi-layer PCB.

In one embodiment the first and second field distribution are gradient field distributions that form a net gradient field.

In one embodiment the field distributions are static magnetic field distributions and the system further comprises a further pair of the above described coils, wherein the field distributions of the further pair of coils are RF field distributions.

In an embodiment the pair of coils is provided in a multi-layer PCB and the further pair of coils is also provided in a multi-layer PCB. In one embodiment both pairs of coils are provided in the same multi-layer PCB.

In an embodiment the, for each coil pair in the system, a driver configured to actuate the first coil and the second coil of the respective coil pair, so that the net field distribution is caused to rotate about an axis perpendicular to the net field distribution.

In an embodiment the system comprises a pair of coils that are configured to jointly generate a net static magnetic field that extends in one direction and a second pair of coils that are configured to jointly generate a net RF magnetic field that extends in a direction perpendicular to the one direction. The drivers are configured so that they cause the rotation of the net RF magnetic field to track the rotation of the net static magnetic field, so that the net RF magnetic field remains perpendicular to the net static magnetic field irrespective of the rotational position of the net static magnetic field.

In one embodiment the direction of a B_o magnetic field is changed by the driver for the pair of B_o coils supplying the B_o coils with currents of relative amplitudes cos(o), -sin(o), wherein a is the desired angle of the B_o field relative to a reference angle. Additionally, in embodiments in which the field gradients rotate with the static magnetic field, gradient coils are supplied with currents of relative amplitudes cos(2o), -sin(2o). In embodiments in which the RF field rotates with the static magnetic field, B1 transmission coils are supplied with currents of relative amplitudes cos(o+P), sin(-o+P), where p is 90o or -90o according to phase cycling schemes.

According to an embodiment there is provided a method of defining a coil comprising: defining the field of one of the coils of the pair of coils in a polar coordinate system as the weighted sum of radial orders of the field, wherein each of the weights applied to a respective radial order in calculating the weighted sum is dependent on the angle in the polar coordinate system; iteratively until a stop criterion has been reached: determining a performance parameter for the coil for a current set of weights used in calculating the weighted sum; and changing the set of weights to improve the performance parameter; determining a wire path of the coil for a field generated based on a final set of weights used in the iteration when the stop criterion is reached.

The angle in the polar coordinate system defines the direction of the generated field in the polar coordinate system relative to a reference angle.

In embodiments the field generated by the thus designed coil can readily be rotated by pairing the coil with an identical coil that is physically rotated relative to the coil and by driving/actuating the two coils in the manner described herein.

In embodiments the weighted sum of radial orders is a weighted sum of radial orders selected from only a single angular order of the field.

By basing the weighted sum on radial orders of only a single angular order, the resulting field is rotationally symmetric. This avoids the need to consider the field generated by the coil at various angular orientations whilst still ensuring rotational symmetry.

By using weights that are cyclically dependent on the angle in the polar coordinate system, field of one coil can be rotated relative to the field of another coil, whilst the field distribution remains identical.

In one embodiment the stop criterion is one or more of a predetermined number of iterative steps having been reached, a cost function having been minimized and the performance parameter having been maximized.

In one embodiment, the method comprises making the coil based on the wire path.

In one embodiment, the weighted sum of radial orders is a weighted sum of radial orders selected from more than one angular orders of the field and wherein the performance parameter is computed based on more than one orientations of the field generated by the current set of weights.

In one embodiment the performance parameter is determined based on a large number, such as >10, >50 or preferably >100 orientations of the field. In one embodiment, the dependence of the weights on the angle comprises for each weight two dependencies of the weight on the angle, wherein the two dependencies complement each other.

Specifically, the two dependencies may complement each other, so that the two weights cyclically change out of phase with each other.

In one embodiment, a first dependency follows the sin convention and a second dependency follows the cos convention.

In one embodiment the dependence of the weight is defined by c₁ sin(e) + c₂ cos(e), wherein and c₂ are the weights that are iteratively changed during optimisation of the coil. It is to be noted that for each radial order the weights and c₂ are independently changed or even optimised.

In one embodiment, the performance parameter is one or more of a field homogeneity, a proxy for the field homogeneity and a representation of the NMR magnetization achievable by the coil.

In one embodiment, the performance parameter is determined by determining a voxel based performance parameter for each of a plurality of voxels in the field of view and wherein the performance parameter is determined based on the voxel based performance parameters.

In an embodiment the performance parameter is the mean, maximum or soft- max of the voxel based performance parameters.

The use of Magic angle spinning in NMR is well known and has become a staple technique when investigating a solid-state sample due to its ability to average-out dipolar coupling in the anisotropic phase, greatly enhancing T2. While Magic Angle Field Spinning NMR has been demonstrated with small samples in homogeneous fields it has not been demonstrated in inhomogeneous fields. Moreover, it requires the rotation of the sample under study at several kHz, an impossible thing to accomplish with humans. Methods of rotating the magnetic field instead of the sample, referred to as Magic angle field spinning (MAFS) are also known. The present disclosure allows implementing MAFS in a one sided/projected field MRI system.

The geometrical reciprocal of rotating a sample at the magic angle to B_o is to create a B_o that rotates in a cone defined by the magic angle (MA). In case of a homogeneous base field B_o in z direction the spinning field takes the form of:

In order to produce a rotating static magnetic field of this nature, three controllable fields (e_x, e_y, e_z) that are perpendicular to each other are required. One of them is given by the B_o direction e_z . In the simple case of having a homogeneous field B_o that should be rotated, the other two fields in e_x, e_y can be created by the classical target field method. However, if the field that should be rotated does not have a homogeneous distribution, the situation becomes more complicated, because the term that describes the field error is no longer a scalar, but a vectorial difference between the desired field in a point and the actual field in a point. Consider the vectorial sum of B_o (B_x, B_y, B_z) and some field G (G_x, G_y, G_z)

If B_o is approximately B_z and |B_OI » |G|, the sum can be sufficiently well- approximated by simply B_z + G_z, which allows one to disregard G_x and G_y, leaving them as degrees of freedom. If the fields norms of B_o and G are roughly in the same order of magnitude, the approximation breaks down and the effect of the above discussed concomitant fields (G_x, G_y) becomes important.

Apart from the solution where both B_o and G are homogeneous, no framework exists to the inventors’ knowledge, that finds the solution for a vector field matching/approximating a desired field.

Moreover, MAFS has, to the inventors’ knowledge, not yet been possible in human MRI due to the limits on the quickest B-field variation allowed by Peripheral Nerve Stimulation (PNS) standards. This value, roughly 80 to 120% of the maximum slew rate of 20T/s, can be approximated as the mean slope of a sine wave during its transition from a peak to a trough, leading to a maximum sinusoidal wave of 5T Hz (i.e. from 5T to -5T in half a period). Given the large fields currently used in clinical MRI, the maximum allowed variation (i.e. a few Hz) would be too slow to provide the benefits of MAFS. The inventors have realised that the advantages of MAFS are more readily obtainable at low static magnetic fields.

A rotationally symmetric system is a system that is physically equivalent to rotation of the sampled object. In a standard high-field MR system, the strong B_o field is applied along one directions, and the inhomogeneous G field gradients are applied along all three spatial directions. When a B_o is applied in one direction (z), the respective coils generating orthogonal gradients G_x and G_y can be designed the same and the combination of the gradient fields they create can be envisaged as single magnetic field gradient that rotates in the plane orthogonal to the direction of the B_o field. G_z is generated by a different type of coil that nevertheless aims to also generate a linear gradient, albeit in the direction of the B_o field. In particular, while dB_z/dx and dB_z/dy are, other in their orientation along the x and y directions respectively, dB_z/dz has inherently different properties. It is known that a true gradient field is impossible to achieve, as it breaks Maxwell conditions, and that consequently undesired magnetic fields (referred to as concomitant fields or concomitant gradients) that accompany the desired gradients are inevitable. These concomitant gradients result in undesired phase accumulation during MRI scans. The concomitant fields effect is inversely proportional to B_o, and whilst it can be ignored in high-field systems, it can have an undesirable effect in lower field strength systems.

Moreover, systems in which the static and varying magnetic fields used for MRI are generated by hardware that is located on a limited number of the sides surrounding the volume of interest may be referred to as projected field systems. Systems in which the hardware that is configured to generate the static and/or varying magnetic fields used during an MRI image acquisition is located on only one side of the volume of interest, for example below the volume of interest, for example in a patient bed, may be referred to as single-sided projected field systems. In an example of a single-sided projected field MR system, the main field during spin evolution, B_o, may be produced by applying current to a PCB, and extends mainly in a direction that is parallel to the plane occupied by the PCB, with little flux extending in a direction perpendicular to this plane, rather than in the z direction.

In summary, in a projected field system and/or in a low field system, creating a pair of rotationally symmetric gradients superimposed on a fixed B_o field is very challenging due to several effects. These are:

- In a projected field setting the hardware components are not distributed around a volume of interest. This limits the field distributions (in particular the homogeneity) that can be achieved with the ‘single sided’ hardware.

- The effect of concomitant fields in low field settings.

- The necessity to generate one gradient along and one across the main/B₀ field direction when imaging is performed in the plane parallel to the PCB that generates the B_o field/in the plane that includes the direction of the B_o field.

The combination of the challenges prevents the standard combination of fixed B_o and varying G coils to create rotationally symmetric field shapes.

In order to overcome or alleviate at least some of the limitation above, in an embodiment both the B_o and the B fields are rotated with each other about an axis that is perpendicular to both the direction of the B_o and the direction of the B field during the course of an imaging experiment. More generally, the rotation can take place about the axis of symmetry or anti-symmetry of the below discussed basis set. In another embodiment the gradient fields are also rotated alongside/together with the B_o and the B fields, creating a symmetrically rotatable system. In yet another embodiment shim field are rotated alongside/together with the B_o, B and gradient fields. In some embodiments higher-order shim fields are also rotated. In the following a rotationally symmetric system is described, alongside and explanation of how this rotationally symmetric system can be used for image encoding by composing of a series of shots, “spokes”, that are designed in a single direction and then applied in many directions.

Fig. 1 illustrates an NMR system 100 with non-rotating B_o field and describe further in Luxembourg patent application no. LU501776, which is incorporated herein by reference in its entirety. The NMR system 100 comprises a dual use coil 110 for creating a static magnetic field, B_o , . . This field is shown to extend in the vertical direction in Fig. 1 , although this is not essential. As is described further below, the dual use coil 110 can be energised and de-energised so that the field B_o , . can be activated and deactivated accordingly.

The system 100 further comprises two coils 120 and 130. The coil 120 also generates a static magnetic field, B_o As can be seen from Fig. 1 , this field extends orthogonally to the field , . As is the case for dual use coil 110, the coil

120 can be energised and de-energ °ised so that the field B_o ^measuremen „t can be activated and deactivated accordingly.

The coil 130 creates a B RF magnetic field at the precession frequency generated by the field The B field extends substantially orthogonally to

B_o Uprepol ,ari .se as well as to the field B u_omeasuremen As is also the case for known NMR RF coils the B field can be activated and deactivated.

The dual use coil 110 and the two coils 120 and 130 are configured so that the magnetic fields B_o . B_o „ and B are generated in a space 142 occupied by an object 140, such as a patient, that is to be made the subject of the NMR measurement.

Whilst a particular configuration of the system 100 is shown in Fig. 1 , the spatial arrangements of the magnet and coils shown in Fig. 1 is not essential, as long as the generated magnetic fields are substantially mutually orthogonal to each other. It will equally be understood that, whilst dual use coil 110 and coils 120 and 130 are illustrated in Fig. 1 as being spaced apart by gaps, theses gaps are only shown for illustrative purposes and that any or all gaps shown may be omitted in a physical implementation of the illustrated system 100 or that some or all of the dual use coil 110 and coils 120 and 130 may instead be provided in a single unit. In one example, the coils 120 and 130 may form part of a single PCB.

Fig. 2 illustrates a known imaging method in a homogenous static magnetic field in which the application of X and Y are gradients allows the readout of signals from the image object in a manner that resembles projections of the signal in various directions across the cross section of the object to be imaged. These “projections” can be used to reconstruct an image of the object. It was realised that a similar imaging technique can be used in embodiments of projected field systems, such as the projected field system shown in Fig. 1 , despite the fact that the degree of homogeneity achievable by, for example, a whole-body bore-type high-field scanner is difficult to achieve in such systems. In particular, it was realised that, if in one embodiment the system 100 comprises coils 110, 120 and 130 arranged in the configuration shown in Fig. 1 and as described hereinbefore, but where these coils are configured to generate respective sy J mmetrically J rotatable ( \about the vertical axis/the direction of B_o Vprepol ,ari .se in Fig o. 1) / B_o u and B fields then imaging in the manner shown in Fig. 2 becomes easier. When referring to a symmetrically rotatable B_o field in the following reference to a B_o field that rotates in a plane orthogonal to the direction of that is in the plane comprising Fig. 1 is made. In addition to the coils shown in Fig. 1 , a system according to an embodiment can also comprise a set of gradient coils. These gradient coils can be planar in the same way as coils 120 and 113 shown in Fig. 1 are and may be provided as three separate planar coil pairs or as a multilayer coil/PCB that comprises the three pairs of coils. The grading coils can be arranged above, below or between the coils 120 and 130 shown in Fig. 1.

In the following numerical methods and practical implementations of the coils and operation system required to manipulate spin for imaging and contrast generation in a projected field and low field setting is described. When referring to a low field a B_o field strength during measurement (excluding any prepolarising B_o field that may be applied) is < 200mT, preferably < 100mT, more preferably < 50 mT and most preferably <10mT. In one embodiment this includes all of the coils influencing the evolution of the spin states I net magnetization vector during an experiment. Fig. 3A shows and example of coil 120 of Fig 1. but configured to generate a symmetrically rotating field B_o. As can be seen from Fig. 3A, the 120 comprises an uncoupled pair of coils 120_x and 120_y. When referring to an uncoupled pair, reference is made to a pair of coils that can be driven electrically independently. In the example, the pair of coils 120 comprises a first coil 120_x and a second coil 120_y. In the example, both coils are planar, tough in other examples, the pair of coils 120 are arranged in a manner that they partially enclose an area of interest. For example, the pair of coils 120 may be arranged on a hemispherical surface. In one example the hemisphere is sized to accommodate the head of an adult, thereby allowing the pair of coils 120 to be used for magnetic resonance of the head/brain. Moreover, whilst the coils 120_x and 120_y are shown as being spaced apart in Fig. 3A, it will be understood that this is for illustration purposes only. In one example, the coils 120_x and 120_y are adjacent to each other. In another example they are abutting each other in an electrically nonconductive manner. In one example the coils 120_x and 120_y are each provided on their own PCB. In another example the coils 120_x and 120_y are provided together in a single multi-layered PCB.

As shown in Figs. 3A and 3B, coil 120_x produces a magnetic field Bo_x that is parallel to the surface of the coil 120_x. The coil 120_y produces a magnetic field Bo_y that is parallel to the surface of the coil 120_y. The magnetic fields Bo_x and Bo_y are rotationally offset from each other by 90°. Whilst the fields are at right angles in the example shown in Figs. 3A and 3B, other offset angles, such as offset angles of 30° or 45° or any integer multiples thereof, are also envisaged.

In the example shown in Figs. 3A and 3B, the pair of coils 100 to produce a static magnetic field B_o. It will be appreciated that, because of the angular offset of the magnetic fields Bo_x and Bo_y generated by the respective coils 120_x and 120_y, the static magnetic field B_o can be caused to rotate about an axis that is orthogonal to the plane occupied by the pair of coils 100. Such rotation is achievable through selective actuation of the coils 120_x and 120_y. In one example, one of the coils 120_x and 120_y is supplied with a sin actuation signal, whilst the other one of the coils 120_x and 120_y is supplied with a cos actuation signal. It will be appreciated that, if offset angles other than 90° are used, then other actuation signals are required to be supplied. It is moreover emphasised that it is not essential that the actuation signals follow a sin of cos function and that other actuation signal functions may be used.

Whilst the arrangement shown in Fig. 3A is above discussed with reference to a B_o coil the B and gradient coils respectively discussed further below have a similar configuration in one embodiment. The symmetrically rotatable coil set disclosed herein encompasses one or more of the following individual concepts:

1. A system of coils capable of producing homogeneous and inhomogeneous (linear and higher-order gradients) magnetic fields in any orientation in a VOL The coils are ordered in uncoupled pairs, such that each pair provides a basis for field generation of a certain order/properties at any orientation. The coils of the B transmit pair are orthogonal to each other, and to the coils of the B_o pair, and may be the same pair. In another embodiment one coil of the pair of coils is used, at a given angle, such as zero degrees, to generate the B_o field whilst the other coil of the pair of coils is used to generate the B field. In another embodiment the pair of coils can be used so that each coil of the pair of coils contributes to the B_o field and the B field whilst maintaining orthogonality between the net B_o field and the net B field jointly created by the pair of coils.

In one embodiment all coils are fully geometrically decoupled from the receive/prepolarisation coil R_x/B₀ , . . This allows to obtain a rotationally symmetric system on a projected field in close proximity to a reception coil. Moreover, the property of rotationally symmetry can additionally be used to produce unique tissue contrast such as that generated by Magic Angle Field Spinning.

2. The gradient pair is configured to create spatial variation on top of the B_o field, and can be rotated with it to produce a 2D rotationally symmetric resolvable information.

3. Alternatively the gradient or the B_o-B₁ setup can be stationary while the other rotates, again producing a 2D resolvable information encoding, albeit not rotationally symmetric.

4. In one embodiment, coils are produced using separate orders. The may be separate Bessel orders, as discussed below. The enable accurate field rotation, for example enabling Magic Angle Field Spinning.

5. The present disclosure provides the basis for arbitrary designed of manufactured fields to be tested for possibility of extension to be used in a rotatable pair/to generate a rotatable field. That is, a coil/field designed in any method, or a coil/field with properties partially or fully dictated by manufacturing constraints, can be projected onto the (Bessel) expansions basis. In that basis, dominant contribution from a single order imply that a coil can be extended into a symmetrically rotatable coil pair.

6. Sequence design is done in an embodiment based on the rotational symmetry property by restricting the design of a spoke to a single projection direction, and extending it to a full sequence by applying spokes on different directions. This allows efficient design of a sequence under arbitrary fields.

7. More generally, the present disclosure provides a method of designing coils that have a field distribution that can be rotated about a predetermined axis. The coils may produce a field distribution that is identical for all rotational positions that can be adopted by it. Alternatively, the field distributions at the various angular positions may deviate from each other to some degree (so that there is imperfect rotational symmetry) but wherein the fields are nevertheless optimised with regard to a specific performance parameter. Such a performance parameter may be the field homogeneity achieved in the various rotational directions.

The design of a coils set for a specific tasks, such as an imaging system, requires searching in a parameter space which can be intractable. As many task are or can be seen as having rotational symmetry (e.g. a circular, spherical, cylindrical target volume or field of view, etc.), the solution can rely on the rotational symmetry. The present disclosure provides a method of designing coils, wherein the size of a search space required to be traversed to arrive at an optimised coil design is reduced when compared to the search space defined by all possible designs.

Fig. 4A shows angular and radial orders of a stream function. When the orders of the stream functions are approximated to discrete wire windings the wiring pattern of a coil producing the order is obtained. The magnetic field generated by the thus produced coil in a plane parallel to the current carrying plane and spaced from it by 5cm is illustrated in Fig. 4B for the individual orders.

Orders j [1.... ,5] on the right -hand side of Figs. 4A and 4B are identical to orders j [1 ,... ,5] on the left-hand side of Figs. 4A and 4B with the exception of a rotation of 90 degrees divided by i. The two coils of the above described uncoupled pair of coils are configured to produce a linear combination of orders j [1 , ... ,5] for a given angular order i on the left-hand side and a corresponding linear combination of orders j [1 ,... ,5] for the given angular order i on the right-hand side of Figs. 4A and 4B respectively. Put in other words, the orders used in defining the behaviour and, with it the wiring pattern of each of the coils in the uncoupled pair of coils will be selected from a single angular order shown in Fig. 4A. Uncoupled coil pairs of this nature allow producing a rotating magnetic field.

It may be advantageous or desirable to overlay a field generated by one angular order with the field generated by one or more other angular orders. In an embodiment this is achieved by producing one pair of uncoupled coils per angular order to be used.

Turning now to the manner in which coils of the nature shown in Fig. 3A are designed/optimised, the magnetic field B(J(c)) generated by a current propagating along a circular path can be defined in a polar coordinate system (r, 0) by: where i [0,1 ,2,...] is the angular expansion order, j [1 ,2,3,...] is the radial expansion orders and, /_; are Bessel functions and is the j^th positive root of J_r C is a set of n x m x 2 coefficients. In one embodiment, only radial expansion orders for one given angular order are combined in any given pair of uncoupled coils, Cy = 0 for all i that do not correspond to the angular order being used.

In another embodiment radial expansion orders with different angular orders can be combined. In the latter embodiment, to still ensure that the field generated by the designed coil facilitates rotation (in the sense that the field does not substantially change with its rotational position) it may not be sufficient to consider the generated field in only one angular direction. Instead, the embodiment evaluates the field in multiple angular directions and maximises a regularisation term B*e_alpha, wherein B is the direction and magnitude of the field generated by the coil using the current set of coefficients and e_alpha is the desired direction of the field for the field direction currently under consideration.

As shown in Figs. 4A and 4B, the expansions are divided into angular and radial orders. In this text, “orders” refer to angular orders, unless otherwise specified. The expansions are divided into 2 sets (the set j=[1 , ... ,5] shown on the left-hand side of Figs. 4A and 4B and the set j=[1 ,... ,5] shown on the right-hand side of Figs. 4A and 4B respectively). This division reflects the sin and cos terms in equation (1). As is clear from equation (1), the sets are rotated versions of the same expansion, with the rotation between the sets being 90 degrees per order.

It is emphasised, that the division into the two sets is arbitrary. More specifically, whilst convenient to use the sin/cos convention of equation (1), using this convention is not essential and other functions for defining fields that, when combined with similar or identical fields in a set of coils as described herein, achieve rotatability of the net field generated could be used instead.

Nevertheless, in the embodiment the sin/cos convention is followed and a linear combination of the expansions according to C is used to form the bases of a stream function, which is then approximated by a discrete wire windings. One way of approximating a stream function using discrete wiring is known from the target field method (R. Turner. A target field approach to optimal coil design. Journal of Physics D: Applied Physics, 19 (8), 1986. URL https://doi.Org/10.1088/0022-3727/19/8/001 , the entirety of which is incorporated herein by reference).

By forming linear combinations of the relevant radial expansions, a desired field distribution (shown in Fig. 4B for the individual orders for a plane parallel to and spaced apart by 5 cm from the plane carrying the field generating current - the net field generated is a linear combination of the fields shown in Fig. 4B) can be generated by a coil.

As coil pair that can rotate the field generated electrically will be composed of two coils, each composed of the same linear combination of expansions of a single angular, in the first and second set, that is, the two coils in the pair are 90 degree/order rotated versions of the same coil. For each rotational direction of the net field generated a, applying currents of amplitudes Asin(a), Acos(a) into the coil pair will result in a field defined by the second coil of the set, rotated by the angle a. Thus, any desired rotation can be achieved in run time using application of appropriate currents.

In one embodiment, an already defined stream function or field can be decomposed/projected into the radial orders according to equation (1). The dominance of a particular angular order suggests that the stream function/field can be used as basis for an uncoupled coil pair as described above to provide a rotating magnetic field.

Coil design for B0 (homogeneous coil)

In the following the design of a coil for B_o configured to generate a predetermined magnetic field strength and that is optimized for reducing field inhomogeneity while preserving the coil power efficiency is discussed. The coil is chosen to have a planar configuration and is required to produce a field along an axis (hereinafter referred to as the x-axis) parallel to the plane occupied by the coil.

The inhomogeneity per voxel was approximated by a proxy for

Ti est F> v) = l/||V(||y normalize F)\\)_v\\ for a field F at location (voxel) v, V is the gradient and where normalize^) if a function that scales a field to achieve a predefined mean magnitude over the FOV. The size of the voxel is chosen to be in the order of magnitude of the size of the pixels to be imaged using the coil. Put in other words, the estimate of the field inhomogeneity is the inverse of the norm of the gradient of the field magnitude at the specified location, y is the reduced gyro-magnetic ratio of the element for which T₂ est is to be determined. T₂ est is in seconds.

In order to provide an estimate of the effective T₂ f°^r reconstruction over all rotations of the field, T₂ rot est '^s calculated over a set fields F resulting from rotations of F where the averaging is over F e F and maxval is a relevant max value for the T2’, such as several seconds, above which increased field homogeneity would not contribute (such as if T2’ was larger than T2). In an embodiment the field generated by a coil is optimised by over the set of coefficients C on the Bessel expansion basis. This optimisation may be done using known optimisation methods, such as gradient descent optimisation. A cost function that can be used for this optimisation method is: + power(C) where Fields(-) produces a rotated fields set from coefficients C, Ty _{rot est} '^s calculated for all individual voxels in the FOV, the spatial reduction function is a function that transforms the Ty _{rot est} values calculated for the various pixels into a single value to be used as part of the cost function and power( ) is a penalty term that factors the power used by the coil into the optimisation process. The spatial reduction function may be the mean, maximum or soft-max of the various Ty _{rot est} values calculated for the various pixels.

In embodiments in which the radial orders are not chosen solely from one angular order the cost function may additionally include the above mentioned regularisation term, B*e_alpha, wherein B is the direction and magnitude of the field generated by the coil using the current set of coefficients and e alpha is the desired direction of the field for the field direction currently under consideration. To optimise the coil for rotational symmetry the sum of the individual/per spoke regularisation term is calculsaded and used as part of the cost function.

Coil design for B1 (homogeneous coil)

In an embodiment a version of the above discussed B_o coil physically rotated by 90 degree is used as starting point. The coil is tested and optimized for excitation efficiency, that is, for the retained magnetization in the plane perpendicular to the local B_o direction, after a delta pulse. A delta pulse here is of an infinitesimal duration and total moment to produce a 90 degree flip angle on average over the FOV.

To determine the retained magnetization within a voxel the voxel is partitioned in a spatially isotropic equispaced manner into sub-voxels, at the center of which the effect of the delta pulse on isochromats is calculated, according to the local B_o and (candidate) B field directions. For this purpose, the same voxels and voxel sizes as used for the optimisation can be used. Doing so is, however, not essential. For each voxel, the voxel’s net magnetization is calculated by summing the contribution of all of the isochromats inside the voxel. The ratio of the net magnetization perpendicular to the B_o direction in the centre of the voxel to the net magnetization on the B_o direction before the pulse is referred to as the retained magnetization.

Based on the retained magnetisation the coefficients C for the coils of the uncoupled pair of B, generating coils are optimised using known optimisation algorithm, such as the gradient descent algorithm and a cost function that optimises for retained magnetization. In one embodiment the cost function used is:

Cost (C (5)

= spacia

+ power( wherein the spatial reduction function is a function that transforms the retained magnetization(C) values calculated for the various pixels into a single value to be used as part of the cost function and power( ) is a penalty term that factors the power used by the coil into the optimisation process. The spatial reduction function may be the mean, maximum or soft-max of the various retained magnetization(C) values calculated for the various pixels.

Coil design for Gradient (1st order inhomogeneous coil)

To enable localisation, a coil for generating a gradient field to work with the B_o field is also generated. In one embodiment the gradient field is optimised along a 1 D strip through the centre of the FOV, with the gradient coil aiming to produce a linear field magnitude gradient when combined with the field generated by the B_o coil. To this end the optimisation carried out is: where Field( ) produces a gradient field by combining the radial order expansions according to the coefficients C as set out in equation (1), diff( ) is a discrete derivative over the 1 D strip, and std( ) is the standard deviation function. In one embodiment a penalty is added to optimize power efficiency in the manner described above with reference to equation (4). It is to be noted that, whilst the cost function of equation (6) optimizes over a 1 D strip that traverses the FOV, the gradient field is optimized over a 2D plane in another embodiment.

Fig. 5A shows a B_o field generated by a single optimised coil of the pair of uncoupled B_o coils described above. Fig. 5B shows a gradient field generated by a single optimised coil of the pair of uncoupled gradient coils as also described above. Fig. 5C shows one way of combining the B_o field of Fig. 5A and the gradient field of Fig. 5B. Fig. 5D shows the same field as Fig. 5C but in this figure the 1 D lines along which the field strength is evaluated in Fig. 5D are indicated. As can be seen, the gradient field is linear along the line A across its centre and otherwise symmetrical with respect to this line.

Fig. 5F illustrates the combined rotation of the B_o and gradient field combination shown in Fig. 5C. As discussed above, the B_o field is generated using an uncoupled pair of coils that can be independently actuated so that they jointly generate a B_o field that rotates about an axis orthogonal to the plane occupied by the figure. The gradient shown in Fig. 5B which equally forms part of the combined field shown in Fig. 5C is also generated using an uncoupled pair of coils in which each coil can be actuated separately so that the gradient field is rotated together with the B_o field. The rotation of the combined field is shown in Fig. 5F.

Fig. 5G shows a different combination of the B_o field shown in in Fig. 5A and the gradient field shown in Fig. 5B. Fig. 5H illustrates the rotation of this combined field. As is the case for the rotation of the combined field shown in Fig. 5C, the rotation of the field in Fig. 5H produces a field that only differs in its angular rotation.

Manufacturing constraints

It will be appreciated that in some situations a desired field distribution is already known. This may, for example, be the case where manufacturing or design constraints limit the field distribution that can be chosen. For the purpose of preparing a coil that generates any such pre-existing field distribution for manufacture the pre-existing field distribution F’ is projected onto the Bessel expansions basis set, as discussed above. The dominance of a single order is tested, by measuring the relative sum of squared field vectors derived from the dominant element alone. In this manner, a linear combination of order generating the desired field distribution can be determined. The preparation for manufacturing process is repeated and tweaked until a sufficiently symmetric rotatability is achieved.

Pulse sequence

Fig. 6 shows an example of a pulse sequence that, in one embodiment, is used with uncoupled pairs of B_o coils, gradient coils and B coils. The uncoupled pairs of B_o coils are provided with a drive signal that generates the fields B_Ox and B_Oy respectively, resulting in a combined B_o filed that can be oriented in any desired direction.

The uncoupled pair of B, coils is equally supplied with drive signals that generate individual fields B_lx and B_ly respectively that combine to a B field for spin excitation. To maximise the signal available, the drive signals are configured so that, in the VOI, the resulting B is substantially perpendicular with the B_o field used for the particular run of the sequence. Put in other words, in one embodiment, the B field is configured to rotate with the B_o field. In one embodiment, the drive pulses for the B coils are configured to maximise retained magnetization, as discussed above. Whilst Fig. 6 shows the use of a spin echo sequence, it will be appreciated that this is merely illustrative of an embodiment, that embodiments are not limited to spin echo sequences and that, instead, other, known NMR pulse sequences can be used as part of the rotating field acquisition method described herein.

Finally, the signals applied to the uncoupled pair or to the plural uncoupled pairs of gradient coils are such that the combination of the B_o field and the gradient field rotates in the manner illustrated in Figs. 5F and 5H. Based on Fig. 5E, it will be appreciated that the gradients applied using the uncoupled pair of coils may not be linear across the entire field of view. Whilst the use of linear gradients in the context of the known method shown in Fig. 2 allows the direct application of the signals shown in Fig. 2 to linear k-space, even the presence of non-linear gradients of the manner shown in Figs. 5 allows determination of the source of NMR signals based on the known gradient distribution and mapping to non-linear k-space.

The pulse sequence shown in Fig. 6 is part of a radial k-space acquisition process and is applied repeatedly whilst the direction of the B_o, B and gradient fields are changed between repetitions. The different repetitions produce different spokes in radial k-space. In one embodiment the direction of the field generated by each coil pair is dependent on the ratio of the signal amplitudes applied to the two coils of the pair. In one embodiment for the B_o and B coil pairs the ratio of signal amplitude sin(theta):cos(theta) generates a field in the direction defined by theta and for the gradient coil pair the ratio of signal amplitude sin(2*theta):cos(2*theta) generates a field in the direction defined by theta.

Image reconstruction

The properties, including frequency, amplitude and phase of the NMR signal generated at a specific location depend on, amongst other factors, such as the chemical environment at the location in question, on the fields used in exciting the NMR signal. These fields, in turn are determined by the hardware used in generating them and by the signals used in driving the hardware. For a given set of coils and excitation parameters, the relevant field properties at a given location at a given point in time are known. The local excitation and reception properties of the NMR apparatus may be considered their local signature.

The NMR signal received during an NMR experiment is a linear combination of the signal generated at individual locations within the field of view of the NMR experiment as modified by the local signature. By acquiring NMR signals in different radial directions (for each of which the local signature is known) an image can be reconstructed

Sequence design

Given that the field of the coil is designed to be the same irrespective of it’s rotational direction, a pulse sequence for use with the coil can be designed by considering the coil’s performance in one angular direction only. The choice of the type of pulse sequence can be made freely and depends on the clinical information the NMR image is intended to convey. Once the sequence type has been chosen, the selected sequence if optimised to maximise a performance parameter, preferably on or more of the signal to noise ratio, image contrast, encoding power and reconstruction accuracy, over a predetermined space, preferably a 1 D projection of the sample. The design of the pulses in one embodiment optimises one or more or all of pulse durations, pulse types, pulse amplitude and gradient combinations.

To this end, only a single BO (e.g. BOx), and single B1 orthogonal to the BO field (e.g. B1y) and a gradient coil combination (e.g. a linear combination of G1 and G2) need to be used. Once a single shot of the sequence has been optimised, the sequence is expanded by applying each shot of the sequence designed initially to a set of rotations. The set may be equispaced or arbitrary distribution of rotation angle. In one embodiment the choice of rotation sets is similarly optimized to maximise one or more of contrast and encoding power on a 2D basis.

While certain arrangements have been described, the arrangements have been presented by way of example only, and are not intended to limit the scope of protection. The inventive concepts described herein may be implemented in a variety of other forms. In addition, various omissions, substitutions and changes to the specific implementations described herein may be made without departing from the scope of protection defined in the following claims.

Claims

CLAIMS:

1 . A method of magnetic resonance image acquisition, comprising: repeatedly: generating a static magnetic field that has a first direction in a field of view, a gradient magnetic field and an RF excitation field that has a second direction in the field of view, wherein the second direction is substantially perpendicular to the first direction; and obtaining an NMR signal caused by the RF excitation field; wherein at least one of the first direction and a direction of the gradient magnetic field is changed between repetitions; and wherein, when the first direction is changed, the second direction is also changed so that it remains substantially perpendicular to the first direction in each repetition.

2. The method of Claim 1 , further comprising changing the direction of the gradient magnetic field between repetitions, so that a way the gradient magnetic field modifies the static magnetic stays the same, irrespective of the first direction adopted by the static magnetic field.

3. The method of Claim 1 or 2, further comprising overlaying the static magnetic field with a further static magnetic field to generate a net static magnetic field that, by virtue of the changes in the first direction over the repetitions, adopts positions on a cone defined by the magic angle.

4. A pair of coils comprising a first coil and a second coil, wherein the first and second coils are configured to generate identical field distributions that are rotated relative to each other, the field distributions of the first and second coils jointly generating a net field distribution, wherein the first and second coils are independently actuable and wherein the field distributions are configured so that actuation of the coils allows the net field distribution to rotate about an axis perpendicular to the net field distribution.

5. The pair of coils of Claim 4, wherein the first and second field distribution are gradient field distributions that form a net gradient field.

6. A coil system comprising the pair of coils of Claim 4, wherein the field distributions are static magnetic field distributions, the system comprising a further pair of coils of Claim 4, wherein the field distributions of the further pair of coils are RF field distributions.

7. The coil system of claim 6, further comprising the pair of coils of claim 5.

8. A system comprising the pair of coils of Claim 4 or 5 and, for each coil pair in the system, a driver configured to actuate the first coil and the second coil of the respective coil pair, so that the net field distribution is caused to rotate about an axis perpendicular to the net field distribution.

9. A method of defining a coil comprising: defining the field of one of the coils of the pair of coils in a polar coordinate system as the weighted sum of radial orders of the field, wherein each of the weights applied to a respective radial order in calculating the weighted sum is dependent on the angle in the polar coordinate system; iteratively until a stop criterion has been reached: determining a performance parameter for the coil for a current set of weights used in calculating the weighted sum; and changing the set of weights to improve the performance parameter; determining a wire path of the coil for a field generated based on a final set of weights used in the iteration when the stop criterion is reached.

10. The method of claim 9, wherein the weighted sum of radial orders is a weighted sum of radial orders selected from only a single angular order of the field.

11 . The method of claim 9, wherein the weighted sum of radial orders is a weighted sum of radial orders selected from more than one angular orders of the field and wherein the performance parameter is computed based on more than one orientations of the field generated by the current set of weights.

12. The method of claim 9 or 10, wherein the dependence of the weights on the angle comprises for each weight two dependencies of the weight on the angle, wherein the two dependencies complement each other.

13. The method of claim 1 , wherein a first dependency follows the sin convention and a second dependency follows the cos convention.

14. The method of any of claims 10 to 12, wherein the performance parameter is one or more of a field homogeneity, a proxy for the field homogeneity and a representation of the NMR magnetization achievable by the coil.

15. The method of any of claims 10 to 13, wherein the performance parameter is determined by determining a voxel based performance parameter for each of a plurality of voxels in the field of view and wherein the performance parameter is determined based on the voxel based performance parameters.