Tomographic imaging using the nonlinear respon of magnetic particles
Bernhard Gleich 1*&Ju
¨rgen Weizenecker 1*The u of contrast agents and tracers in medical imaging has a
long history 1–7.They provide important information for diagnosis and therapy,but for some desired applications,a higher resolution is required than can be obtained using the currently available medical imaging techniques.Consider,for example,the u of magnetic tracers in magnetic resonance imaging:detection thresholds for in vitro 8and in vivo 9imaging are such that the background signal from the host tissue is a crucial limiting factor.A nsitive method for detecting the magnetic particles directly is to measure their magnetic fields using relaxometry 10;but this approach has the drawback that the inver problem (associated with transforming the data into a spatial image)is ill pod and therefore yields low spatial resolution.Here we prent a method for obtaining a high-resolution image of such tracers that takes advantage of the nonlinear magnetization curve of small magnetic particles.Initial ‘phantom’experiments are reported that demon-strate the feasibility of the imaging method.The resolution that we achieve is already well below 1mm.We evaluate the prospects for further improvement,and show that the method has the potential to be developed into an imaging method characterized by both high spatial resolution as well as high nsitivity.
We first introduce the general concept of magnetic particle imaging (MPI).MPI relies on the nonlinearity of the magnetization curves of ferromagnetic material and the fact that the particle magnetization saturates at some magnetic field strength.If an oscillating magnetic field,called the ‘modulation field’,is applied,with frequency f 1and sufficiently high amplitude A ,the magnetic material will exhibit a magnetization M (t ),where t is time.M (t )contains not only the drive frequency f 1,but also a ries of harmonic frequencies (Fig.1a).The higher frequencies can be easily parated from the received signal by means of appropriate filtering.
If the magnetic particles are also expod to a time constant magnetic field with a sufficiently large magnitude,they saturate and the generation of harmonics is suppresd (Fig.1b).Selective suppression of the harmonics is employed for the spatial encoding as follows.In addition to the modulation field,a time-independent field is superimpod (field plot in Fig.2a)that vanishes in the centre of the imaging device (the field-free point,FFP)and increas in magnitude towards the edges.This field is called the ‘lection field’.If there is any magnetic material at the position of the FFP it will produce a signal containing higher harmonics.But only the magnetic material located at the FFP will respond to dulation field.All other magnetic material remains in the state of saturation.By steering the FFP through the volume of interest,a tomographic image can be generate
d.(As a spatial variation in one direction of one field component is in general accompanied by a spatial variation of another component in another direction,only a single lection field is needed in MPI to obtain a three-dimensional spatial encoding.)The movement can be performed by moving the
whole coil asmbly or by moving the object within the coil asmbly.For simplicity,we assumed a low amplitude of the modulation field.Otherwi,field shifts the FFP significantly.
In summary,to form an image,magnetic tracer material has to be applied to,or introduced into,the object.The object is placed in the lection field,and a weak magnetic modulation field is
LETTERS
Figure 1|Respon of magnetic particles to an external magnetic field.a ,An oscillating magnetic field (H ,modulation field,green curve)is applied to the magnetic material at a single frequency f 1.As the magnetization curve (M ,black curve)is nonlinear,the resulting time-dependent magnetization (red curve)exhibits higher harmonics,as is shown in the Fourier-transformed signal (S ,red bars).b ,A time-independent field is added to the modulation field.The oscillating field does not significantly change the magnetization of the material,as it is always in saturation.In this state,harmonics of the oscillating field are almost non-existent.The grey box indicates tho harmonics ud for image formation.The signal at f 1is not ud,as it is small compared to the superimpod induced modulation field signal,and therefore difficult to isolate.
1
Philips Rearch Hamburg,Ro
¨ntgenstras 24-26,D-22335Hamburg,Germany.*The authors contributed equally to this
work.
superimpod.Finally the object is moved (spatial encoding)to discrete positions and the magnitudes of the harmonics are recorded.An image of the magnetic tracer in the object is directly obtained by mapping the magnitude of the harmonics.
The method described so far is capable of generating images of the spatial distribution of magnetic material.However,the mechanical movement leads to low scanning speed and the signal to noi ratio (SNR)is low owing to the weak modulation field.The mechanical movement is dispensable if three additional orthogonal homogenous magnetic fields,called drive fields,are provided (Fig.2b).The three components of the lection field can be cancelled,at any given point in space,by appropriate adjustment of the three fields.By driving each coil pair with a predefined current waveform,the FFP can be moved on a continuous trajectory over the object.This t-up is analogous to a mechanical motion t-up.
By using drive fields,it is possible to accelerate the movement of the FFP dramatically.For this purpo,a different sinusoidal current with a high frequency is applied to each coil pair.The amplitudes of the currents must be large enough to generate magnetic fields capable of cancelling the lection field at the border of the desired region of interest.The fast FFP movement leads to a rapid local change in magnetization as soon as the FFP pass a location containing magnetic mate
rial.The magnetization change induces a signal in the recording coil that exhibits higher harmonics of the drive field frequencies.This induced signal is sufficient for image reconstruc-tion.The modulation field with low amplitude (Fig.1)is now obsolete.Conquently,the introduction of the drive fields over-comes both drawbacks mentioned above,namely the low encoding speed and the low SNR.
So the spatial encoding can be realized in two ways,as follows:(1)using mechanical movement,or (2)using field-induced movement of the FFP.Furthermore,both possibilities can be combined.This is the situation realized in the prent experimental t-up.
The two-dimensional object ud for imaging consisted of distinct holes filled with an undiluted (0.5mol Fe l 21),commercially avail-able contrast agent (Resovist 11,Schering AG Berlin).Components ud in the prent t-up are illustrated in Fig.2a.In order to form two-dimensional images,the object can be moved in two dimensions using a robot.Additionally,the drive field moves the FFP in the
vertical direction.Two alternative encoding types are demonstrated.First,the robot alone is ud for the spatial encoding (mechanical
FFP movement).However,a drive field (A ¼10mT m 021
)for the generation of the harmonics is ud in place of the low-amplitude modulation field,owing to the higher achievable SNR.Second,the robot provides the spatial encoding in the horizontal direction,while the drive field moves the FFP in the vertical direction.The same experiment was evaluated in both cas,but in the cond ca only a subt of robot scan positions was ud.
Figure 3a shows an image of the object,for the ca of pure mechanical movement of the object.Using a drive field leads to a contribution of neighbouring points to the recorded signal at a given robot position.This means that the simple method for generating an image (for the ca of the weak modulation field)by mapping the magnitude of the harmonics is not appropriate,and a reconstruction is necessary;e Methods ction.英语学习网站大全
aprilfoolIn Fig.3b the drive field encodes vertically and the robot is ud for the horizontal encoding.As the drive field amplitude was not sufficiently high to move the FFP over the whole object,three parate images were reconstructed.They covered the upper,middle and lower regions of the object,and were averaged to form Fig.3b.As a result,the resolution in the vertical direction is better than 0.3mm.In the horizontal direction,the resolution is about 0.5mm,as the derivative of the field component of the lection field in that direction is lower.The resolution in both cas (Fig.3a and b)is the same,although the SNR differs owing to the shorter measure-ment time in the cond ca.
The theoretically expected resolution (R )is given by the
ratio肯尼迪就职演讲
Figure 2|The main components of the experiment,and an MPI scanner concept.a ,The two large rings generate the lection field.Hence,urrent with opposite direction in the upper and lower coil produces the sketched field (field lines and colour coded field magnitude)with the field-free point (FFP)in the centre.The same two rings rve as drive field coils,as urrent is superimpod on urrent.A pair of quadratic recording coils in the centre records the spon (harmonics).b ,The field-generating components are sketched schematically for an MPI scanner capable of encoding purely by drive fields.Two field generators produce the lection field.For each direction in space,two opposing drive field coils are ud.The coils produce a more or less homogeneous field in the centre of the scanner and can therefore move the FFP
.
Figure 3|Reconstructed images of the object for two different encoding types.The true size of the holes is indicated in the lower right corner of the large images.The drawings on the right side sketch the robot positions ud for measurement (bottom)and a true scale image (top).In a ,the data at all 52£52robot positions were ud,whereas in b only the data of 3£52robot positions contribute to the reconstruction.In a ,encoding is purely done by robot movement,although the FFP moves a considerable distance in the vertical direction.In b ,this movement is exploited and the encoding is achieved partly by the drive field.The total measurement time was about 50min,including a pure data acquisition time of 18min for a and 1min for b .Tho spots with low intensity reflect imperfections of the object.
NATURE |Vol 435|30June 2005
LETTERS
2H k /X s ,where H k is field strength at which the material produces substantial higher harmonics,and X s is the largest spatial derivative of a lection field component.A reasonable value for H k may be obtained by equating the thermal energy with the Zeeman
energy of the magnetic particles.Assuming H k ¼0.5mT m 021
,reach-able with particles of 30nm diameter,and the currently ud
X s ¼3.4Tm 21m 021
,the obrved resolution is obtained.
Given that the particles have a reported diameter 11of 4nm it is remarkable that the achieved resolution is so high.For such particles,the Langevin theory 12of magnetism would predict quite smooth
magnetization curves with H k ¼210mT m 021
,leading to a resolution of the order of 10cm.We therefore compared the obrved perform-ance to that of ideal particle enmbles acting according to the Langevin theory.Figure 4shows the calculated normalized signal for particles in the range 10–40nm as a function of the number of the higher harmonics.Additionally,the obrved signal and the noi level are included.The experimental data fit well,assuming that particles of 30nm diameter are responsible for the signal.The iron mass of the signal-generating particles reprents only 3%of the total iron mass.
Thus far,the reconstruction was optimized to obtain the best possible resolution.It can also be adapted to compromi resolution while improving nsitivity.Analysing the signal and noi in Fig.4,we estimate the current detection limit to be about 100m mol Fe l 21for a resolution of about 1mm.This detection limit is already within the range of the allowed dosage for medical u 13.However,improve-ments in magnetic tracers and recording electronics can be expected to lower the detection limit to 20nmol Fe l 21.The potential for improvement of the tracer can be en in Fig.4.The signal could be incread by at least two orders of magnitude (compare red line with dashed ‘40nm’line)by a better initial composition and a particle paration process.Additionally,the electronics offers significant potential for improvement.With an optimized version,we expect an improvement in SNR of between one and two orders of magnitude even for a human-size system.
The detection limit extrapolated above can be verified via com-parison with magnetic resonance imaging (MRI).If the signal is induced by an oscillating magnetization M ,and the object dominates the noi (‘patient noi limited’),the SNR is proportional to M but independent of frequency 14.With the detection limit of 20nmol Fe l 21,the expected magnetization would still be about 5%of a
typical MRI equilibrium magnetization,assuming a proton mag-netization M MRI (1T)¼4£1029T m 021
.So the detection limit esti-mated above ems to be reasonable,as the corresponding MRI signal can be detected.On the other hand,a well tolerated dosage of maghemite particles in humans 13is about 70m mol Fe l 21,resulting in an SNR two orders of magnitude higher than that achieved using MRI.
A high SNR may speed up the image acquisition,provided that an adequate encoding speed is possible.In our experiment,the coding time was rather long,but in principle coding speed can be fast in MPI.This would require the u of three orthogonal drive fields responsible for the FFP movement (Fig.2b),as already mentioned in the basic description.In that ca,the encoding time T for a volume (N £N £N voxel)can be shown to be roughly T ¼N 2/f 1.For a drive field frequency of f 1¼25kHz and N ¼50,an encoding time of the order of 100ms can be achieved.The size in each direction of a volume depends on the maximum possible shift F ¼2A /X s of the
FFP ,which is of the order of 6mm for X s ¼3.4Tm 21m 021skr什么意思中文
and the
女神的英文drive field amplitude A ¼10mT m 021
.For medical applications,a larger field of view as well as a higher coding speed is desired.Drive
field amplitudes of up to 20mT m 021
,and frequencies up to 100kHz,may be ud without harming the patient through heating.To achieve a still larger field of view,an additional,slower movement of the FFP can be superimpod.Using permanent magnets,a
no moremaximum X s of about 3Tm 21m 0
21
ems to be possible for human applications,with reasonable effort.The potential of MPI becomes clear when considering the resolution and the encoding speed,in combination with the high SNR,which can be converted to imaging speed and/or nsitivity.
We have demonstrated the possibility of directly mapping mag-netic material,without relying on the ill-pod inversion problem.This offers new opportunities for imaging magnetic tracers with high resolution and nsitivity.MPI may find a variety of applications,such as medical imaging,crack detection,polymer processing or fluid dynamics.For medical applications,such as vascular or small intestine imaging,the high resolution and nsitivity of MPI can be expected to be advantageous.Furt
hermore,the signal can penetrate tissues virtually unattenuated,allowing the inspection of regions located deep below the surface.Additionally,MPI does not necess-arily require a large scanner.All required magnetic fields may be applied from one side.For a relatively small imaging volume,the scanner itlf may be quite small and inexpensive.Finally,the method for localized interaction could be ud not only for imaging,but also for therapy by local heating 15,16.Further work will be needed to exploit the full potential of this new imaging method.METHODS
Hardware.An outline of the MPI scanner is given in Fig.2a.The field-producing coils of the scanner are parated by 50mm,and do not contain ferromagnetic material.de,the spatial derivative of the lection field X s at the FFP is
3.4Tm 21m 021.The drive field amplitude is 10mT m 021
.The drive field frequency is arbitrarily t to 25.25kHz.The two recording coils are of square shape,with about 16mm side length and a paration of about 16mm.They are surrounded by larger windings with opposite n (not shown in the figure)to compensate the induced voltage due to the drive field.In addition,the recorded signal is pasd through a passive notch filter.After amplification and subquent filter stages,the signal is digitized (12bit 20MHz,type PCI-9812,Adlink Inc.).
A robot (Flachbettanlage 1,Ilautomation KG)is ud to move the sample from the upper left to the lower right corner of a square region (approximately parallel to the page plane in Fig.2a)in subquent horizontal lines.The resulting 52£52data points cover a 9.4£9.4mm 2region.
The first test object was the letter ‘P’,formed by 13holes (diameter 0.5mm,length 1mm)in a flat plastic plate that were filled with the magnetic tracer.In addition,a single hole (reference object)with the same dimensions was filled with tracer and ud as a reference respon of the entire system.Its measure-ment,and later u in reconstruction,accounts for all imperfections of the coils and the complex behaviour of the tracer.Both the ‘P’and the reference object were measured with identical parameters (field amplitudes,frequency,robot path,delay and recording
times).
Figure 4|Normalized signal strength as a function of frequency for
simulated magnetic tracer particles and a commercially available contrast agent.The unit signal intensity is that of hypothetical maghemite particles with a step-like magnetization curve and the same iron amount as prent in the commercial contrast agent,Resovist.The green line shows the measured instrumental noi of the acquisition system at a measuring time of 0.4s.The dashed lines reprent the calculated signal strength assuming a specific diameter (10–40nm)of spherical particles acting according to the Langevin theory 12.The total amount of iron is the same as found in Resovist.Thus,the ‘3%30nm’curve reprents the expected respon of an asmbly of ideal particles (30nm diameter)with an iron concentration 3%that of Resovist.LETTERS
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Reconstruction principles.The two acquired ts of data (‘P’and reference respon)were both ud for reconstruction.The n th harmonic V n (y )of the induced signal,at the robot position vector y ,can be written as:
V n ðy Þ¼ð
G n ðx þy ÞC ðx Þd x ð1ÞHere C (x )is the magnetic particle concentration in the object,being unknown
for the image reconstruction.G n (r )denotes the delta respon of the system,reprenting the induced signal in the n th harmonic of the t-up if an infinitesimally small object is placed at position r .This function includes all the complex dynamics of the magnetic tracer,as well as the shape of the drive field and the recording coils.
Obtaining the delta respon from the reference respon.Owing to the u of a relatively large object (0.5mm diameter),it is necessary to deconvolute the delta respon from the reference respon before starting with the reconstruc-tion.In order to achieve that,the spatial Fourier transform of equation (1)is ud (functions in Fourier space are denoted as the corresponding lower ca letters with caret):
^v
n ðk Þ¼^g n ðk Þ^c *ðk Þð2Þ
After division by the known concentration function ^c
*ðk Þof the reference object,a Fourier back-transformation yields G n (r ).
Matrix inversion.For image reconstruction,a direct inversion of the discretized equation (1)was ud,as it gives more flexibility with respect to data reduction.The induced signal is hence:
V n ðy i Þ¼d 2j [{52£52}
X
G n ðx j þy i ÞC ðx j Þ
ð3ÞHere,x j and y i refer to different measuring positions within the scanning plane,and d 2is a normalization factor due to the discretization.The concentration C (x )in equation (1)was determined numerically for each harmonic n pa-rately,using a zero order regularization scheme 17.This leads to veral complete images of the object.Finally,the mean value over a t of the individual concentration images is computed,and shown in Fig.3a.The grey scale was assigned to the image in a linear way.Black was assigned to the lowest obtained concentration.
Reduced data t inversion.If the robot moves only in one horizontal line,the matrix equation (1)is no longer overdetermined,and all reasonable higher harmonics have to be included in the matrix to be u
d for inversion.The new equation can be written as:
V n ðmin Þ¼d 2j [{1£52}
P
G n ðmin Þðx j þy i ÞC ðx j Þ
..
.V n ðmax Þ¼d 2j [{1£52}
P
G n ðmax Þðx j þy i ÞC ðx j Þ
ð4Þ
The inversion was performed in same way as above,but for each of the three lines
independently.Finally,the three images were averaged to form Fig.3b.Received 10January;accepted 12May 2005.
1.Hevesy,G.Radioelements as tracers in physics and chemistry.Chem.News J.Phys.Sci.108,166–-167(1913).
新首页2.Haschek,E.&Lindenthal,O.A contribution to the practical u of photography according to Roentgen.Wien.Klin.Wschr.9,63–-64(1896).
3.Fye,W.B.The coronary angiogram and its minal contribution to cardiovascular medicine over five decades.Circulation 106,752–-756(2002).
4.Hendrick,R.E.&Haacke,E.M.Basic physics of MR contrast agents and maximization of image contrast.J.Magn.Reson.Imaging 3,137–-148(1993).
5.Goldberg,B.B.,Liu,J.B.&Forsberg,F.Ultrasound contrast agents:a review.Ultrasound Med.Biol.20,319–-333(1994).
6.Czernin,J.&Phelps,M.E.Position emission tomography scanning:current and future applications.Annu.Rev.Med.53,89–-112(2002).
上海儿童英语哪个好7.Weissleder,R.&Ntziachristos,V.Shedding light onto live molecular targets.Nature Med.9,123–-128(2003).
8.Heyn,C.,Bowen,C.V.,Rutt,B.K.&Foster,P.J.Detection threshold of single SPIO-labelled cells with FIESTA.Magn.Reson.Med.53,312–-320(2005).
9.Nunn,A.D.,Linder,K.E.&Tweedle,M.F.Can receptors be imaged with MRI agents?Q.J.Nucl.Med.41,155–-162(1997).
10. al.Magnetic nanoparticle relaxation measurement as a novel tool for in vivo diagnostics.J.Magn.Magn.Matter 252,387–-389(2002).11.
squeeze是什么意思
al.Magnetic iron oxide particles coated with carboxydextran for parenteral administration and liver contrasting.Pre-clinical profile of SH U555A.Acta Radiol.38,584–-597(1997).
现在几点了翻译12.Chikazumi,S.&Charap,S.H.Physics of Magnetism (Wiley,New York,1964).13. al.Superparamagnetic iron oxide:pharmacokinetics and toxicity.Am.J.Roentgenol.152,167–-173(1989).
14.Vlaardingerbroek,M.T.&den Boer,J.A.Magnetic Resonance Imaging Ch.6.4(Springer,Berlin,2003).
15.Gleich,B.Method for local heating by means of magnetic particles.World patent WO200418039(4March 2004).
16. al.Effects of magnetic fluid hyperthermia (MFH)on C3H mammary carcinoma in vivo .Int.J.Hyperthermia 13,587–-605(1997).
17.
Press,W.H.,Teukolsky,S.A.,Vetterling,W.T.&Flannery,B.P.Numerical Recipes in C (Cambridge Univ.Press,1992).
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/reprintsandpermissions.The authors declare no competing financial interests.Correspondence and requests for materials should be addresd to B.G.(bernhard.)or J.W.(juergen.).
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