traveling wave magnetic particle imaging

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400 IEEE TRANSACTIONS ON MEDICAL IMAGING, VOL. 33, NO. 2, FEBRUARY 2014 Traveling Wave Magnetic Particle Imaging Patrick Vogel*, Martin A. Rückert, Peter Klauer, Walter H. Kullmann, Peter M. Jakob, and Volker C. Behr Abstract—Most 3-D magnetic particle imaging (MPI) scanners currently use permanent magnets to create the strong gradient eld required for high resolution MPI. However, using permanent magnets limits the eld of view (FOV) due to the large amount of energy required to move the eld free point (FFP) from the center of the scanner. To address this issue, an alternative approach called “Traveling Wave MPI” is here presented. This approach em- ploys a novel gradient system, the dynamic linear gradient array, to cover a large FOV while dynamically creating a strong magnetic gradient. The proposed design also enables the use of a so-called line-scanning mode, which simplies the FFP trajectory to a linear path through the 3-D volume. This results in simplied mathe- matics, which facilitates the image reconstruction. Index Terms—Gradient array, magnetic particle imaging (MPI), tomographic imaging, traveling wave. I. INTRODUCTION M AGNETIC particle imaging (MPI) is a new tomo- graphic method to quantitatively determine the spatial distribution of superparamagnetic iron–oxide nanoparticles (SPIOs). MPI is based on the nonlinear response of ferro- and superparamagnetic particles to alternating magnetic elds. In this method, a eld free point (FFP) generated by a strong gradient (1–7 T/m) is rapidly moved over the sample. Spatial Manuscript received August 02, 2013; revised October 04, 2013; accepted October 06, 2013. Date of publication October 11, 2013; date of current ver- sion January 30, 2014. This work was supported in part by the German Fed- eral Ministry of Education and Research (BMBF) under Grant FKZ 1745X08, through the IDEA project of the 7th framework programme of the European Union (Project 279288) and in part by the German Research Council (DFG) under Grant BE 5293/1-1. Asterisk indicates corresponding author. *P. Vogel is with the Department for Experimental Physikcs 5, University of Würzburg, 97074 Würzburg, Germany, and with the Institute of Med- ical Engineering, University of Applied Sciences Würzburg, Schweinfurt, 97070 Würzburg, Germany, and also with the Research Center for Mag- netic Resonance Bavaria e.V., MRB, 97074 Würzburg, Germany (e-mail: [email protected]). M. A. Rückert and P. Klauer are with the Department for Experimental Physikcs 5, University of Würzburg, 97074 Würzburg, Germany, and also with the Institute of Medical Engineering, University of Applied Sciences Würzburg, Schweinfurt, 97070 Würzburg, Germany (e-mail: martin.rü[email protected] wuerzburg.de; [email protected]). W. H. Kullmann is with the Institute of Medical Engineering, University of Applied Sciences Würzburg, Schweinfurt, 97070 Würzburg, Germany (e-mail: [email protected]). P. M. Jakob is with the Department for Experimental Physikcs 5, University of Würzburg, 97074 Würzburg, Germany, and also with the Research Center for Magnetic Resonance Bavaria e.V., MRB, 97074 Würzburg, Germany (e-mail: [email protected]). V. C. Behr is with the Department for Experimental Physikcs 5, University of Würzburg, 97074 Würzburg, Germany (e-mail: [email protected]. de). Color versions of one or more of the gures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identier 10.1109/TMI.2013.2285472 encoding thereby utilizes the fact that the signal is generated only in the vicinity of the FFP [1]–[3]. Since the rst publication introducing MPI in 2005 by Gleich and Weizenecker [1], several MPI scanner concepts have been proposed. However, most existing concepts use permanent mag- nets that are assembled with the identical poles facing each other to create an FFP [3]–[6]. This creates a so-called selection-eld, which generates an FFP with a strong magnetic gradient. Elec- tromagnetic drive-coils (Helmholtz coil pairs with one coil pair for each spatial direction) allow the FFP to be moved from the center [Fig. 1(a)]. The FFP is then typically moved on a 3-D Lis- sajous trajectory covering the region of interest (ROI) [3], [7]. The permanent magnets advantageously provide an intrinsi- cally high magnetic gradient strength without using any addi- tional electrical energy. However, due to the drive-coils neces- sary for such concepts, moving the FFP through the ROI re- quires large amounts of electrical energy 1 . This results in a high specic absorption rate (SAR) when large elds of view (FOV) are desired. The subsequent stimulation of peripheral nerves and muscles (PNS) can thus become a severe problem in the low kHz frequency range and for the gradient slopes values typically encountered in current scanners [3], [4], [8]. Furthermore, the induced current density and SAR used to combat such problems when a large FOV is required can potentially exceed the restric- tions published by the International Commission on Non-Ion- izing Radiation Protection (ICNIRP) [9]–[12]. A reduction of the SAR is therefore mandatory. One possible approach to solving the SAR issue was pre- sented by Knopp et al. in 2012 [13]. Rather than using perma- nent- or electromagnets in a Maxwell conguration, this con- cept uses two coil assemblies to generate the selection-eld for single-sided MPI [14]. For a given gradient eld strength, this conguration achieves a much lower eld strength outside the FFP, which drastically reduces power consumption and SAR for a given FFP shifting rate. The geometry of the Knopp et al. setup provides a much more accessible sample region in comparison to the setup here presented. The extended eld of view approach presented by Gleich et al. [5] also attempts to increase the FOV within SAR limits. Using additional coil pairs generates a focus-eld that is super- imposed on the static selection-eld. This allows the FFP to be moved to different positions (discrete [5] or continuous [15]) in the scanner. A small FOV, so-called patch, can be captured at each position by moving the FFP with the help of the drive- coils. Additionally, a multi-station image reconstruction method based on the system-matrix, in which one large 3-D volume can be reconstructed from many small sub-volumes (patches) 1 The drive-eld is a sinusoidal, homogenous eld that rapidly shifts the FFP across the FOV. For example, a drive-eld of 40 mT (peak–peak) applied to a 5 T/m gradient would shift the FFP by only . 0278-0062 © 2013 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.

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400 IEEE TRANSACTIONS ON MEDICAL IMAGING, VOL. 33, NO. 2, FEBRUARY 2014

Traveling Wave Magnetic Particle ImagingPatrick Vogel*, Martin A. Rückert, Peter Klauer, Walter H. Kullmann, Peter M. Jakob, and Volker C. Behr

Abstract—Most 3-D magnetic particle imaging (MPI) scannerscurrently use permanent magnets to create the strong gradientfield required for high resolution MPI. However, using permanentmagnets limits the field of view (FOV) due to the large amountof energy required to move the field free point (FFP) from thecenter of the scanner. To address this issue, an alternative approachcalled “TravelingWaveMPI” is here presented. This approach em-ploys a novel gradient system, the dynamic linear gradient array,to cover a large FOVwhile dynamically creating a strong magneticgradient. The proposed design also enables the use of a so-calledline-scanning mode, which simplifies the FFP trajectory to a linearpath through the 3-D volume. This results in simplified mathe-matics, which facilitates the image reconstruction.

Index Terms—Gradient array, magnetic particle imaging (MPI),tomographic imaging, traveling wave.

I. INTRODUCTION

M AGNETIC particle imaging (MPI) is a new tomo-graphic method to quantitatively determine the spatial

distribution of superparamagnetic iron–oxide nanoparticles(SPIOs). MPI is based on the nonlinear response of ferro- andsuperparamagnetic particles to alternating magnetic fields. Inthis method, a field free point (FFP) generated by a stronggradient (1–7 T/m) is rapidly moved over the sample. Spatial

Manuscript received August 02, 2013; revised October 04, 2013; acceptedOctober 06, 2013. Date of publication October 11, 2013; date of current ver-sion January 30, 2014. This work was supported in part by the German Fed-eral Ministry of Education and Research (BMBF) under Grant FKZ 1745X08,through the IDEA project of the 7th framework programme of the EuropeanUnion (Project 279288) and in part by the German Research Council (DFG)under Grant BE 5293/1-1. Asterisk indicates corresponding author.*P. Vogel is with the Department for Experimental Physikcs 5, University

of Würzburg, 97074 Würzburg, Germany, and with the Institute of Med-ical Engineering, University of Applied Sciences Würzburg, Schweinfurt,97070 Würzburg, Germany, and also with the Research Center for Mag-netic Resonance Bavaria e.V., MRB, 97074 Würzburg, Germany (e-mail:[email protected]).M. A. Rückert and P. Klauer are with the Department for Experimental

Physikcs 5, University of Würzburg, 97074 Würzburg, Germany, and also withthe Institute ofMedical Engineering, University of Applied SciencesWürzburg,Schweinfurt, 97070 Würzburg, Germany (e-mail: martin.rü[email protected]; [email protected]).W. H. Kullmann is with the Institute of Medical Engineering, University of

Applied Sciences Würzburg, Schweinfurt, 97070 Würzburg, Germany (e-mail:[email protected]).P. M. Jakob is with the Department for Experimental Physikcs 5, University

ofWürzburg, 97074Würzburg, Germany, and also with the Research Center forMagnetic Resonance Bavaria e.V., MRB, 97074 Würzburg, Germany (e-mail:[email protected]).V. C. Behr is with the Department for Experimental Physikcs 5, University of

Würzburg, 97074 Würzburg, Germany (e-mail: [email protected]).Color versions of one or more of the figures in this paper are available online

at http://ieeexplore.ieee.org.Digital Object Identifier 10.1109/TMI.2013.2285472

encoding thereby utilizes the fact that the signal is generatedonly in the vicinity of the FFP [1]–[3].Since the first publication introducing MPI in 2005 by Gleich

and Weizenecker [1], several MPI scanner concepts have beenproposed. However, most existing concepts use permanent mag-nets that are assembled with the identical poles facing each otherto create an FFP [3]–[6]. This creates a so-called selection-field,which generates an FFP with a strong magnetic gradient. Elec-tromagnetic drive-coils (Helmholtz coil pairs with one coil pairfor each spatial direction) allow the FFP to be moved from thecenter [Fig. 1(a)]. The FFP is then typically moved on a 3-D Lis-sajous trajectory covering the region of interest (ROI) [3], [7].The permanent magnets advantageously provide an intrinsi-

cally high magnetic gradient strength without using any addi-tional electrical energy. However, due to the drive-coils neces-sary for such concepts, moving the FFP through the ROI re-quires large amounts of electrical energy1. This results in a highspecific absorption rate (SAR) when large fields of view (FOV)are desired. The subsequent stimulation of peripheral nerves andmuscles (PNS) can thus become a severe problem in the lowkHz frequency range and for the gradient slopes values typicallyencountered in current scanners [3], [4], [8]. Furthermore, theinduced current density and SAR used to combat such problemswhen a large FOV is required can potentially exceed the restric-tions published by the International Commission on Non-Ion-izing Radiation Protection (ICNIRP) [9]–[12]. A reduction ofthe SAR is therefore mandatory.One possible approach to solving the SAR issue was pre-

sented by Knopp et al. in 2012 [13]. Rather than using perma-nent- or electromagnets in a Maxwell configuration, this con-cept uses two coil assemblies to generate the selection-field forsingle-sided MPI [14]. For a given gradient field strength, thisconfiguration achieves a much lower field strength outside theFFP, which drastically reduces power consumption and SAR fora given FFP shifting rate. The geometry of the Knopp et al. setupprovides a much more accessible sample region in comparisonto the setup here presented.The extended field of view approach presented by Gleich

et al. [5] also attempts to increase the FOV within SAR limits.Using additional coil pairs generates a focus-field that is super-imposed on the static selection-field. This allows the FFP to bemoved to different positions (discrete [5] or continuous [15])in the scanner. A small FOV, so-called patch, can be capturedat each position by moving the FFP with the help of the drive-coils. Additionally, a multi-station image reconstruction methodbased on the system-matrix, in which one large 3-D volumecan be reconstructed from many small sub-volumes (patches)

1The drive-field is a sinusoidal, homogenous field that rapidly shifts the FFPacross the FOV. For example, a drive-field of 40 mT (peak–peak) applied to a5 T/m gradient would shift the FFP by only .

0278-0062 © 2013 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission.See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.

VOGEL et al.: TRAVELING WAVE MAGNETIC PARTICLE IMAGING 401

Fig. 1. From MPI to TWMPI: (a) MPI device based on the basic concept by Gleich and Weizenecker [1]: Two permanent magnets (red/green) create the FFP inthe center of the scanner. Using additional drive-coils (cyan) allows the FFP to be moved through the sample but results in a small FOV. (b) Focus-field methodsimilar to the extended FOV approach presented by Gleich et al. [5]: The permanent magnets are replaced by a number of electromagnets (selection-field coils).Each of these coil pairs (gray/yellow) can be successively used to generate a FFP at different positions in the scanner. A small FOV (sub-volume) can be obtainedwith the help of drive-coils. The combination of all sub-volume FOVs results in an extended FOV. (c) These two concepts (a and b), selection-field plus drive-fieldand the focus-field are the basis for the dynamic linear gradient array (dLGA), which combines the advantages of both approaches.

[16], is applied. While this approach can be used to bypassSAR issues and create a larger FOV, covering multiple patches(sub-volumes) of the FOV increases the overall measurementtime. Furthermore, reconstructing the combined FOV is morechallenging than reconstructing a single FOV [17]–[20].Another acquisition technique is the so-called field-free-line

(FFL) method by which, instead of a FFP, a FFL is used to coverthe FOV. This approach can profoundly improve the sensitivity[21]–[23], i.e., the same sensitivity of a given FFP system couldbe achieved at slower acquisition speed (for a given gradientstrength) and hence less SAR. Nevertheless, the FFL generationand control is more challenging.This paper presents a new approach to overcome the limita-

tions (small FOV, high power consumption and a high SAR)of common MPI scanners. A novel gradient system, the dy-namic linear gradient array (dLGA), combines the function ofthe drive-coil setup [1] with the advantage of the focus-field ap-proach [5] (Fig. 1) andwas designed to enable both efficient FFPgeneration and fast, dynamic movement of the FFP through theROI.The presented traveling wave concept creates two FFPs with

opposite slopes. As the FFPs simultaneously travel along lineartrajectories through the 3-D volume, the trajectory and thus thereconstruction of the dataset are substantially simplified andthe acquisition time is reduced. Moreover, the application ofthe presented approach enables the FOV to be arbitrarily ex-tended in one dimension without increasing the SAR or periph-eral nerve stimulation (PNS).

II. METHODS

A. Traveling Wave MPI

The dLGA is an improvement on the original MPI scannerconcept using drive-coils for signal generation [1] and the focus-field approach [5] extending the FOV (Fig. 1). The presentedsystem, Traveling Wave MPI (TWMPI), requires neither per-manent magnets to create a FFP with a strong magnetic fieldgradient nor additional drive-coils to move the FFP in one di-mension ( -direction).

In a first step, the permanent magnets used for generatingthe selection-field were replaced by several electromagnetic coilpairs [Fig. 1(b)]. These selection-coil pairs were used to movethe FFP to discrete positions inside the ROI and cover sub-volume FOVs using the drive-coils. This step resembles thefocus-field approach [5].To enable a time efficient coverage of large FOVs, the number

of selection-field coils was increased and combined to obtainan array of single coil elements [Fig. 1(c)]. Each coil elementwas theoretically able to be individually driven and designed tocreate a magnetic field sufficiently high enough to saturate theSPIOs.To both generate and move the FFP, a sinusoidal current

(main frequency: ) with an increased phase for con-secutive coils was applied to each element in the dLGA. Thephase difference between adjacent elements was adjusted sothat the current distribution described a wave ( ) spatiallyextended over one wavelength along the -direction of thedLGA [Fig. 2(a)]. This resulted in a linearly moving sinusoidalmagnetic field wave traveling in the -direction.With this concept, two different FFPs are generated: one with

a positive and one with a negative gradient slope. Both FFPsmove approximately linearly through the sample volume alongthe symmetry axis [Fig. 2(b)].The magnetic field and the field gradient are nearly constant

over a large spatial range approximately half the length of thedLGA (simulation, data not shown)2. Thus, for a FOV with alength of 65 mm in the -direction and a diameter of 25 mm, thedLGA should be longer than 130 mm. The dLGA used in thepresented experiments was 143 mm long with an inner diameterof 54 mm [Fig. 2(a)].The distance between two successive FFPs is approximately

half the length of the dLGA. Because the dLGA length corre-sponds to a full wave length, the maximum length of the FOVcan be derived from this restriction when using a single receive

2The dimensioning for a dLGA follows the equation , whereis the effective radius of the single coil dLGA elements. This results in a

good compromise between the magnetic field strength, the gradient strength andthe homogeneity in the center of the dLGA system using a field distribution of(homogeneous area: approximately half the length of the dLGA system).

402 IEEE TRANSACTIONS ON MEDICAL IMAGING, VOL. 33, NO. 2, FEBRUARY 2014

Fig. 2. (a) The dLGA dynamically generates the FFP. Consecutive coil elements are driven with a phase difference so that the current distribution describes a fullwave ( ) along the dLGA. This results in a traveling magnetic field with two FFPs moving continuously along the symmetry axis (traveling wave concept). Thegreen region represents the usable FOV inside the dLGA. The dimensions of the dLGA are chosen to obtain a FOV covering a mouse-sized sample. (b) Simulationof the magnetic field inside the dLGA at two different time points depending on the frequency of the dLGA. The dark regions represent the two FFPstraveling along the symmetry axis: one with a positive and one with a negative slope ( and ).

Fig. 3. Line-scanning mode (LSM): (a) The two FFPs ( and ) travel linearly along the symmetry axis (Point samples: cyan/blue; FOV: green).(b) The point samples inside the scanning line generate the MPI signal twice (once per FFP) for a complete period. Thus, the FOV is scanned twice in one period( ). (c) The acquired data can be easily deconvolved using a suitable 1-D-point spread function (PSF) and Wiener deconvolution.

coil. To acquire the signal from only one FFP at a time, the sen-sitive region of the receive coil must be smaller than the distancebetween two consecutive FFPs (Fig. 2). Thus, the dLGA com-bined with the traveling wave concept intrinsically allows theso-called line-scanning mode (LSM), in which a 1-D line alongthe symmetry axis of a sample is scanned.Due to the two linearly traveling FFPs with opposite gradient

slopes, the MPI sample signal is generated twice, once positiveand once negative, within one period [Fig. 2(b)]. As the FFPsmove over the sample, the magnetization of the sample flipsfrom negative to positive saturation and vice versa. Thus, foreach point in the sample, the induced signal in the receivecoil has a positive and a negative sign within one period[Fig. 3(a) and (b)].After filtering out the excitation frequency ( ), the ac-

quired signal directly reveals the sample in the time domain con-volved with a specific point spread function (PSF). The PSF de-pends on the orientation of the receive coil, the particle-systemand the shape of the FFP [Fig. 3(b)] [16], [24]. This results ina 1-D MPI signal that can be easily deconvolved using a PSFand Wiener deconvolution [Fig. 3(c)]. The 1-D deconvolution

kernel (PSF) required for reconstruction can be measured usinga point phantom or directly computed using Chebyshev polyno-mials and the Langevin-theory [16].

B. 3-D TWMPI

The aforementioned scanner can cover a 3-D volume whenequipped with two additional perpendicular saddle coil pairs:one pair for the - and one for the -direction [Fig. 4(d)]. Toachieve 3-D coverage of the FOV, the 1-D LSM is extended byprogressively shifting the scanning line through the 3-D volume.The shifting is enabled through application of a constant currentto the orthogonal saddle coil pairs [Fig. 4(a)–(c)].Applying a constant offset field perpendicular to the dLGA

main field shifts the FFPs away from the symmetry axis. Dueto their opposite gradient slopes, each FFP is shifted into oppo-site directions [Fig. 4(a)] so that the two FFPs travel along twodifferent trajectories and scan two different lines of the samplein one period [Fig. 4(b)]. Applying two orthogonal offset fields

VOGEL et al.: TRAVELING WAVE MAGNETIC PARTICLE IMAGING 403

Fig. 4. (a) Sketch of the magnetic field inside the dLGA. Applying an offset field in the -direction shifts the two different FFPs into directions opposite thesymmetry axis. (b) Applying discrete values for the -offset field progressively moves the trajectories of the two FFPs through the ROI. (c) Using an additionaloffset field in the -direction, the trajectories of the FFPs are progressively moved along the -direction. A full 3-D volume can thus be covered. (d) Sketch of theTWMPI scanner: Consecutive coil elements of the dLGA (blue 1) generate the traveling magnetic field containing two FFPs along the -axis. Two perpendicularsaddle coil pairs (red/green 3, 4) progressively move the FFPs away from the symmetry axis. The receive coil (cyan 2) is oriented parallel to the main field of thedLGA. (e)LSM: The saddle coils progressively move the scanning line through the volume of interest. (f) Images from the first TWMPI scanner: top: the dLGAconsisting of 16 elements with 4 additional coils for decoupling. Bottom: rapid-prototyped saddle coil system with the integrated receive coil.

allows arbitrary shifting of the scanning lines in the - and -di-rections [Fig. 4(c) and (d)]3. Finally, all lines of the two FFPs arecombined to obtain a full 3-D volume [Fig. 4(c) and (e)].The LSM is the simplest way to scan a 3-D volume using a

TWMPI scanner.

C. TWMPI Control

The dLGA was simplified to test the feasibility of the abovedescribed TWMPI concept. Instead of using 16 independentcoil elements, the system was created to run with only four in-dividual sections (dLGA-4), each consisting of four elements[Fig. 5(a)], with a phase shift of 90 between adjacent sections.Due to this simplified setup, it was possible to run the dLGA-4system with only two independent channels. Thus, controllingthe dLGA-4 system was simpler than the full dLGA system(dLGA-16).

3The two orthogonal saddle coil pairs are placed inside the dLGA and thereceive coil is placed inside the saddle coils. The homogeneity of the saddlecoils is sufficient to accurately move the scanning line through the 3-D volume.The combined receive and saddle coil body was printed in a rapid-prototypingprocedure [Fig. 4(f)].

Because of the strong coupling between neighboring coil ele-ments, it was challenging to establish a defined alternating cur-rent with a fixed phase difference between adjacent coil seg-ments. Consequently, it was necessary to fully decouple the dif-ferent sections to run the dLGA in a stable mode. Only two ad-ditional segments on each end (adjustable distance between seg-ments: ; coupling factor ) were necessary to decouplethe simplified dLGA-4 system as the coupling between two sec-tions is (Fig. 5).

D. Field Performance, SAR, and PNS

The field and gradient strength, the field homogeneity andthe linearly moving FFPs of the dLGA-4 hardly vary (centervariation: approximately 7%) from the simulated data of thedLGA-16 (data not shown).System parameters:With a current of (500W for

the main field), the dLGA-4 generates a traveling magnetic fieldof approximately with a gradient strength of approxi-mately 4 T/m (frequency: ) inside the FOV.

404 IEEE TRANSACTIONS ON MEDICAL IMAGING, VOL. 33, NO. 2, FEBRUARY 2014

Fig. 5. (a) Simplified dLGA (dLGA-4): Rather than using 16 individual segments, only four sections, each consisting of four elements, were individually drivenwith a 90 degree phaseshift between adjacent sections. Two additional coil elements with a distance of were used to decouple the two channels of the dLGA-4.(b) The corresponding circuit diagram shows the coupling factors of this simplified dLGA system. To decouple the two channels of the system, two additionalsegments on each end (adjustable distance between segments: ) are mandatory. Additionally, the sum of the coupling factors must be zero.

The dimension of the FFP is primarily dependent on the mainfield strength. According to Gauss’s law for magnetism4, theFFP is shaped like a pancake with an approximately 6 mm di-ameter ( - and -directions) and approximately 3 mm in height( -direction). The size in the - and -directions is exactly twiceas large as the size in -direction due to the radial symmetryof the magnetic field generated by two coil elements and thesecond of Maxwell’s equations (Gauss’s law for magnetism).This states that the divergence of the magnetic flux is zero[25]

(1)

One solution for (1) is

(2)

with due to the radial symmetry in respectto the -direction. Consequently, the gradient strengths in the- and -directions are half the gradient strength in the -direc-tion . Another solution of (1) gives the geometry for the FFLscanner design [23].The main field strength allows the two FFPs to be deflected

approximately away from the symmetry axis. The twosaddle coil pairs were designed to generate a magnetic field ofca. at a current of , yielding an approx-imate displacement of 0.8 mm per 0.5 A and a power of about200 W for each direction.The chosen system parameters resulted in a FOV (approxi-

mately 65 mm length and 25 mm in diameter) ideal for a mouse-sized sample.The expected resolution of the FFP depends on the gradient

strength and is 4.6 times wider in the - and -directions thanin the -direction [24]. Resolutions of approximately 3 mm inthe -direction and approximately 13.8 mm in the - and -di-rections are thus to be expected.

4For a gradient strength of approximately 4 T/m, the FFP size in the -di-rection would be approximately 3 mm. All calculations in the experiment werecompleted under the assumption that SPIOs are nearly saturated at a magneticfield of approximately 7 mT.

Comparing the SAR performance of a common MPI scanner[3] (gradient strength: 2.5 T/m; drive-fields: ; fre-quency: approximately 25 kHz; FOV: 20.4 12 16.9 )with a TWMPI (LSM) scanner (gradient strength: 2.5 T/m;field amplitude: ; main frequency: 20 kHz) results insimilar SAR values (common MPI: 2 W/kg; TWMPI (LSM):2.5 W/kg, FOV: 65 25 25 ). In both cases the FOVcan be extended further, either by focus-fields, or by elongatingthe dLGA.

III. RESULTS

In a preliminary measurement, a point sample slice wasscanned with 17 full scanning lines to obtain the point spreadfunction (PSF) of the TWMPI system. The data acquired foreach 1-D scanning line, which contained raw-data from the

and the (scanning line parts), were drawnpixel by pixel on a 2-D strip the width of the FFP size anddouble the length of the FOV [Fig. 6(a)]. After correcting thenegative slope of the data, the two parts of each linescan were symmetrically drawn onto a 2-D surface the size ofthe full FOV.In theory, the -position of the scanning lines is given during

the scanning process (representing the trajectory for each FFP:positive for and negative for by the offset fieldapplied in the -direction [Fig. 6(b)]. Due to the width of theFFPs and the distance between two adjacent scanning lines, thelines overlapped 4.4 mm, which is half their width. The datawere therefore subsequently drawn with weighing and normal-ization of the overlapping regions.Since the measurement of a point sample filled with undiluted

Resovist (approximately 4 mm length and 4 mm in diameter0.45 mmol(Fe)/ml, Bayer Schering, Berlin, Germany) showedgood agreement with the simulated dataset of a point sample[Fig. 6(c)], the measured PSF was thus used for the 2-D decon-volution.In this method, each saddle coil pair is individually controlled

with a constant current for line-by-line scanning of a full 3-Dvolume. For the -direction, the current ranges from 0 A to 8 A.For the -direction, the current ranges from to 8 A (stepwidth: 0.5 A). This results in a 3-D dataset with

VOGEL et al.: TRAVELING WAVE MAGNETIC PARTICLE IMAGING 405

Fig. 6. (a) The MPI signal is generated twice per period: once from the with a positive and once from the with a negative gradient slope. Thedata are drawn pixel by pixel on a 2-D strip the width of the FFP and double the length of the FOV. Next, the data are corrected for the negative slope.(b) Depending on their offset fields, the corrected data are cut into two parts and symmetrically assembled with an overlap. (c) Comparison of the measured andsimulated raw data of a point sample (PSF).

Fig. 7. (a) Two orthogonal slices of a full 3-D dataset (35 35 1-D scanning line parts). The slices (I shows the - -slice and II the - -slice) show the rawdata of two samples, each filled with 50 undiluted Ferucarbontran (Meito Sangyo Co. Ltd.). (b middle) The reconstructed images show the line-by-line 1-Ddeconvolved ( -direction) images of the two perpendicular slices. The smearing in the - and -directions is caused by the pancake-shaped FFP and the magneticfield inhomogeneity of the saddle coil pairs at maximum power. (b bottom) Deconvolved image using a suitable 2-D-PSF andWiener deconvolution. The smearingartifact in the - and -directions is reduced.

full 1-D scanning lines5, yielding a total of 35 35 1-D scan-ning line parts from the two different FFPs. These can then beretrospectively combined to obtain one single 3-D dataset. InFig. 7(a), two slices [with different orientations processed as inFig. 6] of a 3-D dataset are shown. Also depicted are the raw dataof two point samples filled with 50 undiluted Ferucarbon-tran ( , Meito Sangyo Co. Ltd., Nagoya,Japan). Both point samples were 6 mm long with a diameter of4 mm. One of the samples was placed in the symmetry axis andthe second was placed with an offset of approximately 6 mmfrom the axis and approximately 14 mm from the first sample.Fig. 7(b) (middle) shows the reconstructed slices after a

line-by-line 1-D deconvolution in the -direction. Due to thepancake-shaped FFPs and the magnetic field inhomogeneity

5The number of required scanning lines can be calculated by, where represents the number of scanning line

parts covering the FOV in both directions.

of the saddle coil pairs at maximum power, the images aresmeared along the - and -directions. However, the structureand the size of the two sample points can be observed.Reconstruction quality can be improved using a 2-D decon-

volution [using a simulated 2-D PSF, Fig. 6(c)] instead of aline-by-line 1-D deconvolution (Fig. 7(b), bottom). As seen inthe figures, smearing along the - and -directions has beenvisibly reduced and the sample structure is clearly discernible;however, the resolution could not be additionally improved [24].Furthermore, a 3-D deconvolution would also be unable to no-ticeably increase the image quality or the resolution in this case.There are, however, novel approaches to overcome these issues[26].The acquisition time for each single 1-D scanning line was

(with). For the full 3-D volume, the scanning time in-

creased to ( ).

406 IEEE TRANSACTIONS ON MEDICAL IMAGING, VOL. 33, NO. 2, FEBRUARY 2014

IV. DISCUSSION

The new gradient system (dLGA) is a linear array of singlecoil elements that dynamically combine the advantages of theselection-field and the focus-field approaches. Thus, the dLGAcan be arbitrarily extended in the axial direction without in-creasing the SAR or PNS of the MPI measurement.Compared to systems using permanent magnets or Maxwell

coil pairs as suggested by Gleich and Weizenecker [1], [3], thedLGA has a higher energetic efficiency when the FOV is in-creased in the axial dimension. Thus, the power consumptionfor the dLGA grows only linearly instead of quadratically asoccurs with common MPI scanner configurations. When dou-bling the dLGA length in the -direction by doubling the coil el-ements and holding the phaseshift constant (current distributiondescribes a wave ( ) spatially extended over two wavelengthalong the dLGA length), the magnetic field and the gradient arenearly constant over 75% of the length of the extended dLGA(simulation, data not shown)6. The FOV length is tripled in the-direction. Thus, extending the FOV by a factor of 3 only dou-bles the required electrical energy.Since the magnetic field amplitude, gradient, speed of the

FFPs and the bandwidth remain the same, the SAR and PNSare kept constant. Thus, when keeping the phaseshift betweenadjacent elements constant, the FOV contains three FFPs. Toavoid data ambiguity, a separate receive coil for each FFPwouldtherefore be necessary, resulting in a constant acquisition time(parallel MPI with acceleration factor 3).The presented TWMPI approach can cover a mouse-sized

sample in a very short measurement time. A 3-D volume ap-proximately 65 25 25 can be acquired in

, where is the number of averages,the frequency of the dLGA, and the number of desiredscanning lines in the - and -directions. With ,

and , the scanning time for a full 3-Ddataset would be . This, for example, would enableresolution of different points in the mouse heart cycle (500 beatsper minute) while respecting SAR and PNS limitations.Unfortunately, simple control of the numerous dLGA ele-

ments is hindered due to each element having a constant phasedifference in relation to neighboring elements. It is possible toavoid this coupling issue by reducing the control channels ofthe system through the combination of single coil elements intosections (dLGA-16 vs. dLGA-4).Adding two perpendicular saddle coil pairs to the dLGA con-

verts the system to a 3-D scanner and thus enables the scanningline to be progressively moved through the entire FOV. As it isdirectly used for signal generation, however, the dLGA shouldbe driven at high frequencies when using the LSM. This is be-cause the induced signal increases with frequency while simul-taneously decreasing the acquisition time.The main frequency of the dLGA must be chosen so it is

high enough to obtain a strong inductive MPI signal from theSPIO ensembles. Because of the coupling between the dLGA

6The length of the FOV can be calculated with the equation:. Where is the length of the dLGA system and is the

wavelength of the current distribution over the dLGA coil elements.

elements, building the dLGA for stable operation at high fre-quencies and high currents (at least ) is challenging.Although the preliminary tests of the LSM at a main frequencyof provided low signal, the feasibility of thismethod was nevertheless demonstrated.In the future, using litz wire for the dLGA elements could re-

duce the energy loss and heating issues caused by the skin-effectat higher frequencies. Moreover, the saddle coil pairs could beplaced outside the dLGA to further increase the usable FOV andthe magnetic field homogeneity.The LSM intrinsically provides a simple method for scan-

ning a large FOV and only a basic 1-D deconvolution with thePSF is necessary to reconstruct the image. However, to decreasesmearing caused by the FFP shape, the measured data (Fig. 7)demonstrated the necessity of additional deconvolving in the -and -directions. While a 2-D deconvolution can significantlyincrease the image quality of the reconstructed data, the res-olution cannot be increased using this scanning mode and re-construction method. Advanced trajectories of the FFPs could,however, eventually overcome this limitation.

V. CONCLUSION AND OUTLOOK

This work introduces a new concept of magnetic particleimaging: the Traveling Wave MPI. Based on a low energygradient system for MPI devices, this system offers a largefield of view without using permanent magnets. The presentedtraveling wave concept in combination with the line-scanningmode enables a fast and energy efficient method for covering alarge 3-D volume in one MPI session.The TWMPI devices offer new approaches to MPI and can

solve issues found with current scanners.The homogeneity of the dLGA could also be used to provide

static magnetic fields, enabling future combinations ofMPI withmagnetic resonance (MR). For example, a Golay-setup couldserve as the MR gradient system and the dLGA could create thefield.

ACKNOWLEDGMENT

The authors would like to thank A. Basse-Lüsebrink andT. Basse-Lüsebrink for tidying up English grammar and ex-pression in this manuscript.

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