WO2016182446A1

WO2016182446A1 - Detecting magnetic objects in magnetic resonance images using phase saddles

Info

Publication number: WO2016182446A1
Application number: PCT/NL2016/050345
Authority: WO
Inventors: Johannes Gijsbertus BOUWMAN; Peter Roland SEEVINCK
Original assignee: UMC Utrecht Holding BV
Current assignee: UMC Utrecht Holding BV
Priority date: 2015-05-13
Filing date: 2016-05-13
Publication date: 2016-11-17
Anticipated expiration: 2017-11-13

Abstract

A method of object detection in MRI comprises determining a filter representing an effect of an object in a frequency domain with respect to phase of a plurality of sampled data points of an MRI dataset (401) based on at least one phase saddle in a combined phase gradient field that is a combination of a phase gradient field caused by the object based on a shape and material of the object and a phase gradient field caused by an image sequence used to generate the MRI dataset. The filter is applied to a phase component of the sampled data points in the frequency domain. The effect of the object can comprise a change of the phase caused by the object.

Description

DETECTING MAGNETIC OBJECTS IN MAGNETIC RESONANCE IMAGES USING PHASE SADDLES

FIELD OF THE INVENTION

The invention relates to medical imaging with Magnetic Resonance Imaging (MRI), more precisely to the visualization, detection and localization of internal compact diamagnetic, paramagnetic, or ferromagnetic objects.

BACKGROUND OF THE INVENTION

Accurate localization of diamagnetic or paramagnetic objects in magnetic resonance (MR)-scans can be necessary during image guided intervention; for example, to visualize catheter markers, internal fiducial markers, to detect and localize brachytherapy seeds and SPIO clusters. The past decade has seen growing interest in methods to selectively localize compact objects with a deviating magnetic

susceptibility compared to that of human tissue with positive contrast. An embedded magnetic object or marker can affect the acquired MR signal, due to two properties: It has no internal hydrogen atoms, and its magnetic susceptibility is different than that of the surrounding medium. Previously reported methods to detect and localize magnetic objects within a body, all make use of these two properties and the mentioned effects.

One such a method is Pattern Matching based on forward simulations. In this approach the complete effect of the object on the acquired signal is simulated with Bloch equations. To this end, a numerical model of the marker is made available, and the simulations are performed in high resolution for all possible orientations of the markers and/or possible background field gradients. Objects or markers can then be automatically detected within a volumetric 3D image by autocorrelation, in which the location are returned having the highest spatial match with a specific template. In the case of cylindrical objects or markers, for a variety of different orientations, separate correlation procedures can be performed, while returning the orientation with the highest match.

Other related art that makes use of gradients in the phase near the magnetic objects are Susceptibility Gradient Mapping (SGM) and Phase Gradient Mapping (PGM). SGM quantifies/detects this gradient locally with a short term Fourier Transform, and PGM detects these gradients by taking the derivative of the phase image in the spatial domain.

Further related art makes use of gradients in the altered spin frequency distribution, center-out RAdial Sampled Off-Resonance (coRASOR) imaging cancels the transversally induced field gradients by a set of radial field gradients during sampling, which leads to a circular ring of signal pile-up which can be radially refocused by a radial phase ramp in the frequency domain. White Marker imaging (WM) and GRadient echo Acquisition for Superparamagnetic particles with Positive contrast (GRASP) cancel the longitudinally induced field gradient during slice selection, which dephases all signal within an imaging slice but the location in which this applied gradient is cancelled by the induced gradient.

Other methods directly make use of the altered spin frequency, by adapting the frequencies of the radio pulse. Frequency Selective Excitation makes use of specific excitation pulses that only excite the high or low frequencies present near the marker. Inversion-recovery with ON-resonant water suppression (IRON) first blocks (saturates) the regular frequencies, and then excites the high and low frequencies in the vicinity of the marker. In this way, only atoms close to the object are flipped to the transversal domain, and the signal can be localized by spatial encoding.

Another group exploits the induced offsets in the accumulating phase distribution, for example with a dedicated acquisition with Fast Low Angle Positive contrast Steady-state free precession (FLAPS) or with Iterative Decomposition of water and fat with Echo Assymmetry and Least-squares estimation (IDEAL). However, the induced phase offsets can also be exploited on the resulting phase image as a contrast mechanism in Susceptibility Weighted Imaging (SWI), to reconstruct the underlying susceptibility distribution with Quantitative Susceptibility Mapping (QSM).

Many of these related solutions were found to be succesful in generating positive contrast, however, mostly with minor or substantial adverse side-effects. For example, most methods do not yield contrast at the exact position of the perturber (FSX, IRON, WM, GRASP, FLAPS, IDEAL, SGM, PGM), either do not show the underlying anatomy (FSX, IRON, WM, GRASP, FLAPS, IDEAL), either are not based on scantypes which are always clinically available (FSX, IRON, WM, GRASP, coRASOR, FLAPS), depend on processing (coRASOR, SWI, QSM, T2'-imaging, SGM, PGM), depend on a template library which is calculated a priori (Template Matching) or are restricted to specific sequences or trajectories (almost all of them). Taking these shortcomings into account, an ideal positive contrast method gives clear and selective contrast at the position of the perturber with the underlying anatomy visible in the original scan, and can be combined with a variety of clinically available scantypes.

Localizing even simple spherical, ellipsoidal or cylindrical objects, in particular diamagnetic, paramagnetic, or ferromagnetic objects, in MR-scans is not a

straightforward task, as the field induced by such a marker interferes with the spatial encoding of the followed scan protocol. Currently no generic algorithm exists that can selectively depict the location of such markers in any type of MR scan, without priorly simulating how the marker interferes with the followed scan protocol.

Current detection algorithms, however, are restricted to specific scan types, or do rely on the availability of a priorly obtained template library, derived from computationally expensive simulations, which are mostly not flexible to changes in the scan conditions.

The above information is presented as background information only to assist with an understanding of the present disclosure. No assertion is made as to whether any of the above information might be applicable as prior art with regard to the present disclosure. A list of references to prior art documents is presented at the end of this description.

SUMMARY OF THE INVENTION

It is an object of the present disclosure to provide an improved method and system to detect at least one of diamagnetic objects, paramagnetic objects, and ferromagnetic objects in MRI images.

An aspect of the present disclosure provides a method of object detection in magnetic resonance imaging, MRI, comprising

determining a filter representing an effect of an object in a frequency domain with respect to phase of a plurality of sampled data points of an MRI dataset (401) based on at least one phase saddle in a combined phase gradient field that is a combination of a phase gradient field caused by the object based on a shape and material of the object and a phase gradient field caused by an image sequence used to generate the MRI dataset; and applying this filter to a phase component of the sampled data points in the frequency domain.

The effect of the object may comprise a change of the phase caused by the object.

The step of determining a filter representing the effect of an object in the frequency domain with respect to phase of the sampled data points may comprise determining the combined phase gradient field in a spatial domain.

The at least one phase saddle may occur in the combined phase gradient field in predetermined locations with respect to the object.

The step of determining the filter may comprise finding the positions of the at least one saddle, and calculating the phase values in the at least one saddle.

The step of applying the filter may comprise applying a phase correction to the MR data in the frequency domain.

The object can have a magnetic susceptibility different than that of tissue.

The object can be a spherical object.

The phase gradient field caused by the object can be a dipole field such as, for example, caused by a spherical magnetic object, or a deformed dipole field as caused by, for example, an ellipsoidal or cylindrical magnetic object.

The phase gradient field caused by the image sequence can be a linear phase gradient field.

The the combined phase gradient field may comprise three saddle points.

Another aspect of the present disclosure provides a system for object detection in magnetic resonance imaging, MRI, comprising

means for determining a filter representing an effect of an object in a frequency domain with respect to phase of a plurality of sampled data points of an MRI dataset (401) based on at least one phase saddle in a combined phase gradient field that is a combination of a phase gradient field caused by the object based on a shape and material of the object and a phase gradient field caused by an image sequence used to generate the MRI dataset; and

means for applying this filter to a phase component of the sampled data points in the frequency domain. Another aspect of the present disclosure provides a computer program product comprising instructions for causing a computer system to perform the method set forth hereinabove.

The person skilled in the art will understand that the features described above may be combined in any way deemed useful. Moreover, modifications and variations described in respect of the system may likewise be applied to the method and to the computer program product, and modifications and variations described in respect of the method may likewise be applied to the system and to the computer program product. BRIEF DESCRIPTION OF THE DRAWINGS

In the following, aspects of the invention will be elucidated by means of examples, with reference to the drawings. The drawings are diagrammatic and may not be drawn to scale. Similar items may be indicated with the same reference numeral throughout the drawings.

Fig. 1 illustrates how the dipole and the spatial encoding creates phase saddles.

Fig 1 illustrates an effect of a spherical marker on a gradient.

Fig 2 illustrates a reference frame for spatial encoding.

Fig 3 illustrates a process of obtaining a phase shift for an ellipsoidal marker. Fig 4 illustrates an example implementation in a framework.

Fig 5 illustrates an example of the phase distribution around a marker.

Fig 6A illustrates examples of the simulated effect of a marker.

Fig 6B illustrates examples of the derived filter in k-space.

Fig 6C illustrates an example of a resulting positive contrast image.

Fig 6D illustrates a contrast image after high-pass filtering and zero-filling.

DETAILED DESCRIPTION OF EMB ODFMENT S

An aspect of the present disclosure is to provide a method of object detection in MRI imaging, comprising determining a filter representing the effect of an object in the frequency domain with respect to phase of the sampled data points; and applying this filter to a phase component of an MRI dataset in the frequency domain.

The effect of the object can comprise a change of the phase caused by the object. The step of determining a filter representing the effect of an object in the frequency domain with respect to phase of the sampled data points may comprise: determining a change in a phase gradient field caused by the object based on a shape and material of the object; determining a change in a phase gradient field caused by an image sequence used to generate the MRI dataset; and determining the filter by combining these two gradient fields.

The step of determining a filter representing the effect of an object in the frequency domain with respect to phase of the sampled data points may comprise determining a combined effect of a phase gradient of a spatial encoding and a phase gradient of the object in the frequency domain.

The determined combined effect may comprise a change of the phase of a sample point in the frequency domain MRI dataset.

The step of determining a combined effect may be performed based on phase saddles occurring in the combined effect in predetermined locations with respect to the object.

The object may have a magnetic susceptibility different than that of tissue, for example the object comprises a metal object. Examples of tissue include organic tissue such as human tissue.

The object can be a spherical object.

The the phase gradient field caused by the object may be a dipole field such as, for example, caused by a spherical magnetic object, or a deformed dipole field as caused by, for example, an ellipsoidal or cylindrical magnetic object.

The phase gradient field caused by the image sequence may be a linear phase gradient field.

The filter may comprise three saddle points.

According to an aspect of the present disclosure, a system is provided comprising means for performing steps recited hereinabove.

According to another aspect of the present disclosure, a computer program product is provided that comprises instructions for causing a computer system to perform the steps of any preceding method claim.

An aspect of the present disclosure is to provide an accurate, generic and fast method to localize known and unknown internal spherical, ellipsoidal and cylindrical markers or objects from materials with a magnetic volume susceptibility deviating from that of the surrounding tissue (such as "magnetic markers") within MRI scans, adaptable to local background fields. With this method we can depict these magnetic markers by applying a phase correction ("phase shift") to the acquired raw MR-data in the frequency domain, which -after the inverse Fourier Transform to the spatial domain- leads to a bright spot at the location of the marker. For spherical and cylindrical markers we can also detect the orientation of the marker (polar and azimuthal angle).

The method is accurate as it is based on the physical phenomenon of 'phase saddles', which are three regions where the marker induced phase distribution exactly cancels the applied phase gradient of the spatial encoding. For this relative phase of these saddles with respect to the marker, an analytical solution was derived based on the marker properties (volume, and volume susceptibility) and the scan parameters (k- space trajectory and sampling times).

The method is generic as these phase saddles are present in any combination of marker and scan type.

The method is fast as it works directly on the raw frequency MR-data, by a multiplication with a complex phase shift based on the relative phase of the saddles. Moreover, the needed phase shift in the frequency domain can be calculated explicitly, thereby circumventing the need of simulation the objects behaviour on the signal.

The method allows at least to detect spherical markers by the analytical solution, as well as ellipsoidal and cylindrical markers by a heuristic modification.

The method enables to adapt to variations in both the strength and the shape of the marker as well as possible local background fields.

An aspect of the present disclosure is a method that aims to be a generic algorithm for detecting and localization of any spherical, ellipsoidal or cylindrical objects, in particular diamagnetic, paramagnetic, or ferromagnetic objects, in MR scans suitable for any type of acquistion strategy, while circumventing the need for creating a template library based on numerical simulations. In a particular aspect, the method allows to include the linear component of static macroscopic field gradients.

An aspect of the present disclosure is to provide a generic procedure to detect, localize and identify, for example, internal passive spherical, ellipsoidal and cylindrical objects/markers in MR based on their magnetic strength and the followed scan trajectory using phase saddles. Compared to Pattern Matching based on forward simulations, the presented method can circumvent the need for forward simulations and the need of a template library.

An aspect of the present disclosure provides visualization / localization / detection of spherical/ellipsoidal/cylindrical markers in MR scans by predicting their effect on the phase of acquired MRI data points by using the phenomenon of phase saddles.

An aspect of the present disclosure provides visualization / localization / detection of spherical markers in MR scans by predicting their effect to the phase of an acquired datapoint by using the here presented analytical solution for the calculation of phase saddles.

An aspect of the present disclosure provides visualization / localization / detection of simple markers (spherical/ellipsoidal/cylindrical) in MR scans by predicting their effect to the phase of an acquired datapoint by using a numerical approach to calculate the phase in the phase saddles.

An aspect of the present disclosure provides visualization / localization / detection of ellipsoidal/cylindrical markers in MR scans by predicting their effect to the phase of an acquired datapoint by deriving this from the here presented analytical solution for spherical markers and the herein disclosed transformation from spherical to ellipsoidal/cylindrical coordinates.

In the following, certain aspects of magnetic resonance imaging will be described in greater detail. The detailed description, however, merely serves the purpose to explain and illustrate aspects of the present invention. For clarity of exposition, certain aspects of MRI and its related physical principles have been simplified.

An MRI scanner forms an image of the interior of the human body, by strongly magnetizing this body and then measuring its reaction to a combination of

radiofrequency pulses and changing field gradients.

Internal, magnetized hydrogen atoms can be detected with external electrical coils. In order to obtain these measurements, electrical coils must be placed closely to the side of the body, and the interior of this body must be forced to act like a rotating magnet, which then creates a changing flux in these coils. This internal magnet can be created from the highly abundant hydrogen atoms in the body, which have the property of becoming standing rotating nano-magnets ("spinning tops") when they are exposed to a strong magnetic field.

To create a measurable effect in the coils (changing magnetic flux), we can force these nanomagnets to all rotate synchronously in horizontal planes, which can be done as follows: the main magnetic field first brings them all in the same starting configuration: 1) pointing their magnetic field along the main magnetic field (referred to as the z-direction), and 2) making them spin with a high frequency around this z- direction. Since at this starting configuration the direction of all these nano-magnets are statically pointing upwards, no signal can be detected in the coils. To induce a changing flux in these coils, we force that the direction of these nanomagnets starts rotating in the horizontal plane (x,y-plane). This can be done by sending an electro-magnetic pulse perpendicular to the z-axis, with the same frequency (resonance frequency) as the spinning hydrogens, hence: "magnetic resonance imaging".

The spatial distribution of hydrogen atoms (MR images) can be reconstructed using field gradients. Following the abovementioned procedure we can measure the strength of this collective magnet, however, does not allow to reconstruct the origin of several subgroups of nanomagnets, which would be needed to create an image revealing the spatial distribution of hydrogen atoms in the body. To discern hydrogen atoms from different locations, we force that groups of atoms with a different spatial location have a different effect on the coils.

The first option, is to make only a part of the body sensitive to the transversal flipping, while silencing the rest of the body. This is mostly done by creating a spatial field gradient over the head to feet direction over the body during transversal flipping, having the result that only a slice of the body has the same frequency of atom spinning as the radio pulse for the excitation (slice selection).

The second option is to apply a spatial gradient before signal receiving, which will give distant spins a different phase than proximate spins, which also allows to reconstruct the spatial position in this dimension (phase encoding).

The third option is to apply a spatial gradient during signal receiving, which will give distant spins a different frequency than proximate spins, which in turn allows to reconstruct also the spatial position in this dimension (frequency encoding). By combining slice selection with phase and frequeny encoding, the origin of the measured signal can be reconstructed in 3D, returning a volumetric image of the body.

MR datapoints are measured spatial frequencies, corresponding to coordinates in 'k-space'. To create a typical 3D image of 128 x 128 x 128 voxels, a number of 128 x 128 x 128 complex- valued data-points is acquired, for 128 x 128 x 128 unique combinations of phase and frequency encodings. This complex data is stored in a 3D matrix, for which the coordinates of each dimension are the coordinates of 'k-space'. Coordinate triples in k-space are cartesian wave number vectors, that describe the direction and the strength of the global linear phase gradient that was applied for the spatial encoding at the moment that that specific data point was acquired. This 3D matrix of spatial frequencies can be converted by an inverse 3D Fourier Transform into a 3D spatial image that reveals the spatial proton density.

An embedded magnetic object/marker effects the acquired MR signal, due to two properties: First, it has no internal hydrogen atoms, and therefore this absence of signal has a relative negative effect on the coil (negative contrast). Second, its magnetic susceptibility is different from that of the medium, and therefore becomes a magnet on its own, creating an additional magnetic field in its environment. This changes the rotation frequency of its surrounding, having the following effects on near hydrogen atoms: It changes their reaction to the excitation pulse (their 'resonance'); it influences their spatial encoding (geometrical distortion); gradients in this field may cancel the signal due to mutual cancellation (negative contrast); and accumulated phase difference may be visible in the complex- valued MR images (phase contrast).

The effect of a spherical marker on a specific datapoint: A magnetic object present in the MR field of view has an influence on each acquired datapoint being sampled in the spatial frequency domain. This is illustrated in Fig. 1 for a specific datapoint. Image 102 illustrates the linear phase gradient which is applied by the scanner for spatial encoding of the signal (in the absence of a magnetic object). The direction and the strength of this gradient are indicated by the k-space coordinates. This phase distribution will however be altered by the marker 105 induced phase distribution 101, which is described by the dipole function for spherical markers, and by a 'deformed' dipole function in the case of ellipsoidal and cylindrical markers. Combined, this results in the pattern 103. The net effect of the marker 105 on this specific datapoint can be numerically simulated, by computing the volumetric integral over all spins in the pattern 103, which falls under the category of Bloch simulations. A legend 104 of the used intensity values is also shown, corresponding to the phase in the spatial domain. In the legend 104, the vertical axis represents phase.

Fig. 1 shows an illustration of the phase saddle phenomenon; the gradient

(black arrows 109) of the marker induced dipolar phase distribution (represented in grey scale) around the magnetic object 105 is shown in image 101. This distribution, combined with the linear phase gradient of the spatial encoding (shown in image 102) yields the pattern in image 103. For convex (e.g. spherical, ellipsoidal, cylindrical) objects this creates exactly three phase saddles 106, 107, 108, where this linear gradient is cancelled. As the effect of such an object on the phase of the measured data-point is predominantly determined by the phase of these three saddles, and as these three phase values can be accurately predicted based on the properties of the marker and the followed scan protocol, this allows fast and accurate detection of the marker.

The phase shift caused by a convex object is determined by the phase in the saddles. The net effect on the phase of this specific data point, however, can for this example be estimated from the illustration of image 103; as the spins with zero phase are clearly overrepresented in the image, the net effect of the marker 105 on this datapoint has a phase value of zero. In these three regions 106, 107, 108, the gradient of the phase distribution is zero, which creates an 'isophasic' region in which the phase distribution is spatially stationairy. The phase in such a phase saddle has then a dominant effect on the phase of the acquired datapoint.

Explicit calculation of the phase saddles allows an efficient estimation of the phase shift. The phase in these saddles can be calculated by first finding the positions of these saddles, and then calculating the phase values therein. The positions can be resolved by solving where the marker induced phase distribution cancels the encoding phase gradient. The phases can then be found by summing the marker induced phase with the applied phase of the encoding. The combined effect of these saddles is then roughly the complex average of the three phase values in these saddles. For each datapoint, the phase shift can be calculated from the followed scan protocol and the properties of the marker.

In the following, a phase shift filter for spherical objects is disclosed in greater detail. To this end, it is disclosed how the relative position of the phase saddles can be determined. To determine the phase in the saddles, first the positions of the saddles are found by solving where the combined gradient distribution is zero:

ViPenc + ^ψ-marker ⁼ 0

Herein:

V⁽Penc ⁼ 2nk_enc [rad/mm]

is the linear phase gradient of the spatial encoding (illustrated in image 102), in which k_enc is a 3D vector in the spatial domain denoting the wavenumber [mm^"1] in each dimension:

\ , the azimuthal angle ^aenc ^e [^— π, π and the polar angle 6_enc E [Ο, π].

Fig. 2 shows a reference frame for the spatial encoding and the locations of the phase saddles. All coordinates are relative to the position of the marker 105 (black sphere) at the origin.

The marker induced phase gradient is proportional to the gradient of the dipole function (see also fig la):

and the meaning of the symbols in the above equation is indicated in Table 1. Table 1:

y [rad*s^"1*T¹] The gyromagnetic ratio of the hydrogen nucleus

Bo [T] The strength of the main magnetic field of the scanner

The marker's relative magnetic volume susceptibility with respect to the tissue

V [mm³] The marker's volume

t [s] The 'dephasing time' of the marker (the acquisition time of the sampled data point) which is:

the time relative to excitation in Free Induction Decay scanning and Gradient Read Echo scanning

the time relative to the Echo Time in Spin Echo scanning Θ [rad] The polar angle of relative position to the center of the marker. r [mm] The distance to the center of the marker

There are three positions where the combined phase gradient is zero, which are the positions of the three phase saddles m = {0, 1,2} , relative with respect to the center of the marker.

Herein, the distance of the saddles to the markers center is given by r_m :

3 |P |

(0_m) + 5 cos (0_m)

I 2n:|/L„ 1 - 2 cos²

Herein, the degree of perturbation P of the marker at a given timepoint t is given by: p _≡ γΒρ χν

For the polar angle 0_m of each phase saddle m = {0,1,2} it can be derived that:

From these relative positions the relative phase values in the saddles can be calculated.

The relative phase in the saddles and corresponding correction factor can also be determined. The phase difference between the saddle and the marker is the summated phase difference of the marker induced phase in the saddle and the innerproduct of the position vec \ .

Δψγη ~ ⁽Pmarker m)

Which can be shown to be simplified to:

3 cos

saaaie _{= 4}p . ²0 - i

Complex averaging of these three phase values yields the estimated phase shift.

Applying this negative phase shift yields the positive contrast filter for spherical markers: ψπι

m=0

Although the analytical solution yields the phase values in the exact saddle points, two minor modifications can be added to optimize the contrast. It will be understood that these modifications are entirely optional. The first modification compensates for an observed underestimation of the analytical phase shifts values for low phase gradients and the second modification compensates for an observed overestimation of high phase shift values. Both modifications are implemented in an algorithm for spherical perturbers, that is disclosed hereinafter.

The final shift matrix for spherical objects, incorporating the analytical solutions and the two heuristic modifications is then given in the frequency domain by:

nsaddle

C(k, P(t)) = ∑_m ² ₌₀ e -ⁱ^

With: (_psaddle ₌

3 cos²(0_m)-l

+ 0.6 * sign(m

⁸V(l-2 cos²(e_m) + 5 cos⁴(0_m))³ 1-5)

/

Here the max- function compensates for underestimation of the phase shift in case of low phase gradients, and the term 0.6 * sign(m— 1.5) compensates for overestimation of the phase shift in case of high phase gradients.

The positions of the phase saddles for ellipsoidal markers were derived via a coordinate transformation from that of a spherical marker with equivalent volume and volume magnetic susceptibility, as an analytical solution was not available.

To this end first the volume of the larger hypothetical concentrical sphere on which this 'spherical saddle' is located was determined, and its equivalent ellipsoidal counterpart was determined, with an equivalent large volume, and being confocal with the marker of interest.

On this larger confocal ellipsoid the point is determined with the same tangential plane as the 'spherical saddle' has, with respect to the large sphere.

From the derived position of this 'ellipsoidal saddle' the phase is calculated with the analytical solution for the ellipsoidal structures and the inner product of the newly determined position and the center of the marker. Fig. 3 illustrates how the phase shift for ellipsoidal marker 301 is obtained from the analytical solution for a hypothetical spherical marker with the same volume 302. Step 1) Determination of the radius of the equivolumetric spherical marker. Step 2) Calculation of the saddle position S for this spherical marker. This saddle S lies on a concentric larger sphere 303. Step 3) To determine the position S' needed to calculate the phase shift for ellipsoidal markers, the equivolumetric ellipsoid 304 is determined, which is confocal with the original marker 301, and S' is that unique position on the large ellipsoid having the same normal vector as point S with respect to the sphere 303. The needed phase shift for the ellipsoidal marker is now the relative phase in S' with respect to the phase coding for the center of the ellipsoid, which can be calculated by adding the innerproduct of the vector form S' to the ellipsoids center and the encoding k-vector, together with the analytical field as induced by the marker at S' .

Detecting the orientation of the elongated marker can now be done by first applying the proposed filter for a number of orientations and then by choosing the orientation of the filter that yields the highest match / contrast.

To detect compact or elongated convex structures other than spheres and ellipsoids, such as cubes and cylinders, these can be simplified first to equivolumetric spheres or ellipsoids, and then carrying out the procedure for spheres or ellipsoids.

Local background fields may be incorporated, for the following reason. Static background gradients may decrease the efficiency of the proposed filters for both spherical and elongated objects, however, this can be easily compensated for in the proposed filter.

A significant static gradient in the background field at the location of the marker will have an effect on the performance of the method. Such a gradient can for example be caused by air cavities or nearby metallic implants. At least the linear part of such a gradient, however, can be incorporated in this method, by adapting each k-space vector according to the strength of the local gradient and the sampling time of that specific data-point.

Suppose an additional macroscopic gradient in the frequency distribution, of which the linear component is V(jO_macro

Then over time, this will create an increasing (accumulating) phase gradient: k_macro over time: As the time of each sampled point is assumed to be known for applying this method, the processed k-space coordinates for this algorithm can then be taken as:

^processed ^~ ^encoding ^macro (

To improve the efficiency of the method, this filtering can be done on the specific region of interest in which this macroscopic gradient is presented.

Detection and localization of the objects can be done as follows, for example.

Suppose the complex MR data is S(k, t). Then the positive contrast image is obtained by:

S(k, t) * C(fe, P(t)) \

S(k, t) * C(k, P(t)) \) in which the denominator serves as a necessary high-pass filter. From this image the local maxima will correspond to the best candidates for the detected markers. Subvoxel accuracy can be obtained by taking the weighted average over a subvolume of 3x3x3 voxels, in which the voxel with the local maximum is the central voxel.

Visualization of resulting positive contrast images can be performed as follows, for example. The 3D positive contrast images can be directly interpreted visually by standard Maximum Intensity Projections (MIPs). These visualizations can be

(artificially) enhanced by a (standard) zero-filling in the frequency domain before the Inverse Fourier Transform.

Fig. 4 illustrates an example implementation of the presented method in a framework. In the figure, the proposed filter is implemented in a possible framework, for a situation in which both the marker strength is not precisely known and there is an unknown static background field present near the expected position of the marker. Step 1) First several global filters are calculated for this marker, accounting for some variety in the strength of the marker. Step 2) This creates a sequence of contrast images, in which local maxima correspond for the initial position and strength of the marker. Step 3) Candidates are selected, and from the regularly reconstructed image (4) a subregion (local fields of view) can be selected in the case of string field gradients. Step 5) To apply the local filter, a Fourier Transform is taken from this subregion. Step 6) For GRE: Estimate background field (shifted k-space). 7) Filters are calculated for a chosen variety of possible background gradients, leading to 8) a variety of local contrast images, from which the image is selected with the maximal contrast, from which 9) the final position is determined.

It is preferred that the method has access to the complex raw data (in the spatial frequency domain), and the exact 'scanning coordinates' of each acquired data point, being the k-space coordinate and the acquisition time. In cases when the exact scanning coordinates are not known, the method also works on 'filtered' spatial data, the complex- valued visual (clinically available) output of the scanner, often customly processed (filtered, regridded, zero-filled, apodized, etc) by the reconstruction software of the vendor of the scanner. Although information may be lost in this process, the method also performs on this kind of data, and the consequently

mixed/averaged/regridded scanning coordinates.

The methods work on all type of MR data including data acquired with the following

· trajectories: cartesian, EPI, radial, spiral, kooshball, propellor, etc

• scan types: Free Induction Decay (FID), Gradient Read Echo (GRE), Spin Echo (SE), Turbo Spin Echo (TSE) etc

• acceleration techniques: SENSE, GRAPPA, Compressed Sensing, Multiband Multislice

· dimensionality: 3D and 2D techniques

The core implementation of the method has a proven analytical solution for spherical markers. The heuristic modifications to this analytical solution were verified under many conditions . The method for spherical and ellipsoidal markers has been validated on numerical simulations. The method for spherical markers has been validated in phantom experiments.

It will be understood that although the method is particularly suitable to depict simple convex objects (e.g. spherical, ellipsoidal and cylindrical objects), the present disclosure is not limited to this type of objects.

Aspects of the present disclosure relate to the field of interventional MRI with the aim to depict pointine devices with positive contrast, while keeping image quality high, as in catheter tracking, micro-electrode depiction and the localization of brachytherapy seeds. An aspect of the present disclosure is to derive a general formulation for depicting a known punctiform magnetic marker of interest from potentially any scan type (FID, GRE, SE) of 3D MR-dataset, acquired with any type of trajectory (radial, cartesian, spiral, . . . ).

An approach disclosed herein is to generalize coRASOR to non-radial scans. coRASOR highlights the center of a marker of interest by centrally focusing circular signal pile-up, arising when spherical symmetric objects are imaged with center-out radial scanning. The dependency on radial scans can be alleviated, by explaining the efficacy of coRASOR using the phenomenon of 'phase saddles' ; three regions 101, 102, 103 in the marker's vicinity in which the encoding k-vector is exactly canceled by the marker' s induced field shift (see Fig 5). The preserved signal in these isophasic regions 101, 102, 103 can be shifted to the marker's center, if the phase in these saddles is known, enabling a quantitative positive contrast filter compatible to a variety of scan types.

Fig. 5 is an illustration similar that to 106, however, for a magnetic marker 506 of which the induced phase distribution is opposite to the marker depicted in 106. The phase distribution induced by a magnetic marker 506 cancels the applied k-vector of spatial encoding (diagonal arrows 504) at exactly three positions (ellipses 501, 502,

503), located in the plane spanned by the vectors B₀ (arrow 505) and k_enc . The preserved signal in these saddles can be used to highlight the marker 506 by applying a phase correction to the raw data with the negative value of the relative phase in these saddles in respect to the marker 506.

To calculate the relative phase in the three saddles, first their relative positions were determined. As they were found to lie in the plane spanned by k_enc and B₀, their 2D polar coordinates {0_m, r_m} in this plane were determined by solving

V<Pmarker (@m> ^rm> Ts) + 2nk_enc = 0, with <ji½_arfcer ⁼ P · Here the perturbation P ≡ ^YB^° ^V T_S depends on the marker's volume V and susceptibility Δχ relative to the medium, Bo and the sampling time T_s relative to excitation (FID, GE) or

Echo (SE), and k_enc is expressed in 2D polar form {6_enc, \k_enc \}. An example of the formulas for the three phases cp_m is given in the following equations, which show an example of an analytic formulation of the k-space filter: 1 "²

C(t) = - exp(-i<p_m)

87T|/c_enc| . * 3|P| 3 cos²(0_m) - l

<Pm = si#n(P)

2n\k_enc\ (1 - 2 cos²(6»_m) + 5 cos⁴(0_m))^3/

+ 7 - A

A = sin²(0_enc)

The filter was tested on a numerical phantom with a small perturber centrally located in the FOV. Three different acquisition schemes were simulated including Gradient Echo, Spin Echo, and a center-out scan (kooshball). To further increase the method's contrast and the spatial resolution, the corrected data-points in k-space were respectively normalized to unity and zero-padded before applying the inverse Fourier Transform. A first experimental validation was performed by detecting brachytherapy seeds located in a piece of porcine tissue, which was scanned at 1.5T, [1mm]³ with center-out radials with WFS of 0.243 voxels.

Fig. 6 shows examples of the proposed filter's compatibility to a variety of 3D acquisition schemes, yielding selective positive contrast, especially when combined with high-pass filtering and zero-filling. More particularly, the figure presents a numerical validation of the versatility of the proposed method, by simulating the effect of a marker with a relative susceptibility of 400 ppm and radius 1.5mm scanned at 3T for a GRE acquisition (top row), an SE acquisition (middle row) and center-out kooshball data (bottom row). Shown are the midsagittal planes with Bo vertical, and the read direction horizontal. Fig. 6A shows an example of the simulated effect of the marker, in terms of magnitude (left column) and phase (right column). Fig. 6B shows an example of the proposed filter in k-space, in terms of magnitude (left column) and phase (right column). Fig. 6C shows an example of the proposed positive contrast, in terms of magnitude (left column) and phase (right column).

Fig. 6D shows an example of the contrast image shown in Fig. 6C, however with the low spatial frequencies suppressed (highpass filtered), and with an artificially increased resolution (using zero-filling). Fig. 7 shows experimental results for brachy-seed depiction. The boxes 702 added in the detailed image 701 show the results for coRASOR, showing that isoPHASOR generates finer, more localized contrast. Although not visible in Fig. 7, the proposed filter suppresses the background anatomy more than coRASOR. More particularly, Fig. 7 shows an example of the proposed method applied to brachyseed depiction in heterogenous porcine tissue. The detail image 701, shown on the right of Fig. 7, shows the result of coRASOR, showing that isoPHASOR results in finer contrast. Not visible in this figure, is that isoPHASOR is less sensitive to other other anatomic structures than coRASOR. Moreover, isoPHASOR does not need tuning or optimization, as the optimal strength of the correction factor follows directly from the closed form equations.

Disclosed herein is, inter alia, a positive contrast filter for depicting punctiform objects that is compatible with a variety of different scan trajectories. The formulation more or less unifies several other k-space filters, including the optimal coRASOR phase ramp for center-out scanning, and the Fourier Transform of the complex signal at a given sampling time for GRE pattern matching. The method can depict objects with sufficient magnetic strength to locally cancel the applied phase gradient of the spatial encoding. The explicit formulation based on the scan trajectory and the marker strength may exempt the user from further analyzing or simulating the interaction between the encoding and the marker induced field shift. Directly applicable to raw datasets, the method may circumvent error-prone preprocessing, making the method both fast and robust.

The effect of the object to be detected on the phase of a sampled point in the frequency domain can be predicted using the saddles in the spatial phase distribution that are a consequence of the combination of phase gradients of the encoding gradient and the induced phase by the object to be detected.

A method of object detection in MRI may comprise determining a filter that alters the phase of the acquired MRI datapoints (401) in the frequency domain, thereby undoing the phase effect of that object in the frequency domain, based on phase saddles in the spatial phase distribution, which arise due to the combination of 1) the phase gradient caused by the object based on a shape and material of the object and 2) the phase gradient caused by an image sequence used to generate the MRI dataset; and the method may further comprise applying this filter to a phase component of the sampled data points in the frequency domain.

Some or all aspects of the invention may be suitable for being implemented in form of software, in particular a computer program product. Such computer program product may comprise a storage media, such as a memory, on which the software is stored. Also, the computer program may be represented by a signal, such as an optic signal or an electro-magnetic signal, carried by a transmission medium such as an optic fiber cable or the air. The computer program may partly or entirely have the form of source code, object code, or pseudo code, suitable for being executed by a computer system. For example, the code may be executable by one or more processors.

The examples and embodiments described herein and in the Annexed documents serve to illustrate rather than limit the invention. The person skilled in the art will be able to design alternative embodiments without departing from the scope of the claims. Reference signs placed in parentheses in the claims shall not be interpreted to limit the scope of the claims. Items described as separate entities in the claims or the description in the Annexed documents may be implemented as a single hardware or software item combining the features of the items described.

Legend of Fig. 4:

401 Calculate isoPHASOR filters

402 Calculate contrast images

403 Candidate selection: position (subvoxel) & strength

404 Inverse FT

405 Fourier Transform

406 For GRE: Estimate background field (shifted k-space)

407 Calculate local isoPHASOR filters

408 Calculate local contrast images

409 Final localization: subvoxel position; strength; background field; background phase

References

Topic Article

Pattern Matching Med Phys, 33, 4459-4467 (2006) Susceptibility Gradient Dahnke H. et al, Magn Reson Med;60:595- Mapping 603(2008)

Phase Gradient Mapping Magnetic Resonance in Medicine 62: 1349-1355

(2009)

coRASOR P.R.Seevinck et al, MRM, 65: 146-156(2011)

White Marker Seppenwoolde J-H et al, MRM;50:784-790 (2003)

GRASP Mani et al, Magn Reson Med 2006;55: 126-135.

Frequency Selective Patil et al, In: Proc of the 15th ISMRM, Berlin, 2007. Excitation (FSX) (nr 1122).

IRON Stuber M et al, Magn Reson Med 2007; 58: 1072- 1077

FLAPS Dharmakumar R et al, Phys Med Biol 2006;51 :4201- 4215.

IDEAL Yu H et al, J Magn Reson Imaging 2007;26: 1153—

1161.

SWI Haacke EM et al. (2007). Am Journ of Neuroradiol

28 (2): 316-7.

QSM Dong et al, MRM, 10.1002/mrm.25453

Claims

CLAIMS:

1. A method of object detection in magnetic resonance imaging, MRI, comprising determining a filter representing an effect of an object in a frequency domain with respect to phase of a plurality of sampled data points of an MRI dataset (401) based on at least one phase saddle in a combined phase gradient field that is a combination of a phase gradient field caused by the object based on a shape and material of the object and a phase gradient field caused by an image sequence used to generate the MRI dataset; and

applying this filter to a phase component of the sampled data points in the frequency domain.

2. The method of any preceding claim, wherein the effect of the object comprises a change of the phase caused by the object.

3. The method of any preceding claim, wherein the step of determining a filter representing the effect of an object in the frequency domain with respect to phase of the sampled data points comprises:

determining the combined phase gradient field in a spatial domain.

4. The method of claim 1, wherein the at least one phase saddle occurs in the combined phase gradient field in predetermined locations with respect to the object.

5. The method of claim 4, wherein the step of determining the filter comprises finding the positions of the at least one saddle, and calculating the phase values in the at least one saddle.

6. The method of claim 1, wherein the step of applying the filter comprises applying a phase correction to the MR data in the frequency domain.

7. The method of any preceding claim, wherein the object has a magnetic susceptibility different than that of tissue.

8. The method of any preceding claim, wherein the object is a spherical object.

9. The method of claim 1, wherein the phase gradient field caused by the object is a dipole field such as, for example, caused by a spherical magnetic object, or a deformed dipole field as caused by, for example, an ellipsoidal or cylindrical magnetic object.

10. The method of claim 1, wherein the phase gradient field caused by the image sequence is a linear phase gradient field.

11. The method of any preceding claim, wherein the combined phase gradient field comprises three saddles.

12. A system for object detection in magnetic resonance imaging, MRI, comprising means for determining a filter representing an effect of an object in a frequency domain with respect to phase of a plurality of sampled data points of an MRI dataset (401) based on at least one phase saddle in a combined phase gradient field that is a combination of a phase gradient field caused by the object based on a shape and material of the object and a phase gradient field caused by an image sequence used to generate the MRI dataset; and

means for applying this filter to a phase component of the sampled data points in the frequency domain.

13. A computer program product comprising instructions for causing a computer system to perform the method of claim 1.