Seminar 1a

Magnetic particle imaging

Author:

Jan Malec

Mentor:

prof. Dr. Denis Arcon

Abstract

Magnetic particle imaging is a promising emerging imaging technique that has manypotential advantages over some existing imaging techniques used in the medicine to-day, especially in angiography. Magnetic �elds are used to change magnetization ofsuperparamagnetic nanoparticles and the detected signal is proportional to changes inmagnetization. Human body is mostly diamagnetic, so it does not obstruct the imagingprocess. Most current implementations use a gradient �eld to magnetically saturate allparticles in the scan volume but a few, so we only detect particles in a selected area.Prototype scanners can already achieve sub mm resolution, making it at last comparablewith currently used imaging methods, such as MRI.

August 31, 2015

Contents

1 Introduction with brief history of medical imaging 1

1.1 Motivation for magnetic particle imaging . . . . . . . . . . . . . . . . . . . . 2

2 Magnetic particle imaging 2

2.1 Superparamagnetic particles respond to magnetic �eld . . . . . . . . . . . . 22.2 Detecting changes in magnetization . . . . . . . . . . . . . . . . . . . . . . . 32.3 Spatial selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

2.3.1 Magnetic �elds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52.4 Gridding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

3 Simpli�cations and limitations of the model 7

3.1 Filtering signals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73.2 Relaxation e�ects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83.3 Scaning volume . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

4 Summary 10

1 Introduction with brief history of medical imaging

Following his experiments with the Crookes tubes, Wilhelm Röntgen took and published the�rst medical image[1], a photo of his wife's hand[Figure 1].

Figure 1: First X-rayimage[1]

The invention of X-ray transmission imaging has started a medicalrevolution, as it enabled to see undestructevly inside the body.X-ray transmission imaging is a technique that measures X-rayabsorption parameter and it was at �rst used mostly to view bonefractures and deformations owing to the large contrast between theabsorption coe�cients of bones and soft tissues..

Later, when stronger beams and better �uorescent screens weredeveloped, it was possible to see in vivo motion, as �uoroscopybecame possible. After 1920, radiologists began using radio opaquecontrast agents such as barium to visualize internal organs or veins(angiography).

This method was later upgraded to computed tomography(CT) that combines X-ray projections to construct tomographicslices of the scanned object. This method provides much betterinformation than the traditional X-ray, at a cost of a higher ra-diation dose. Moreover, iodized contrast, used in X-ray and CTangiography is toxic to many patients, especially those su�eringfrom Chronic Kidney Disease. Those patients represent one quar-ter of all patients scanned with this method[2].

In contrast to X-ray transmission imaging, nuclear medicineuses substances, ingested by the patient instead of an external source of radiation. Thesetechniques allow the radioactive substances, called radio pharmaceuticals, to localize speci�corgans or cells, allowing diagnosis of some conditions in very early stages. An obvious

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Figure 2: MPI (orange/red) and MRI (grey) images of a mouse that was injected withcommercially available iron oxide tracer after 30 seconds[2]

drawback to this method is that the patient must ingest radioactive substances that areharmful to the body.

Ultrasound Imaging, developed in 1960s uses re�ecting ultrasound waves to visualizeinternal structures, including muscles, joints, vessels and internal organs. It is still a broadlyused technique, because it districts soft tissue, provides a live image, the machines areportable and it is completely harmless. It's main drawbacks are limited image detail and�eld of view, especially when imaging structures behind bone or air.

Magnetic resonance imaging is a technique that uses external magnetic �elds in whichnuclear magnetization precesses. This precession is then measured as our signal and isrelated to the density of protons. However, given the weakness of nuclear magnetization,the MRI signal remains very weak, thus limiting the sensitivity of this technique. Magneticresonance is preferred over Computer tomography when possible, because it produces noionizing radiation and is therefore completely harmless to most patients. The downsides ofMRI are high operating cost and slow operation.

1.1 Motivation for magnetic particle imaging

Magnetic Particle Imaging (MPI) is a new promising technique. which was developed inthe last 10 years[3], that may solve many of the problems mentioned above associated withthe peculiarities of established imaging methods. This method uses spatially selective �eldsto measure concentrations of magnetic nanoparticles inside the body. It is perhaps the �rstmedical imaging technique developed around a tracer - medically, a substance injected in thepatients blood stream, and not the other way around. The superparamagnetic nanoparticles(SP) are generically not toxic, so MPI is considered a safe imaging method, even for patientswith poor kidney function. Currently built prototype MPI machines have already achievedsub millimeter resolution[4], that is comparable or better than 0.5mm resolution, achievedby CT[1] and 1mm MRI resolution[1]. The high resolution and sensitivity of this techniquesexplores the fact that the human body is mostly diamagnetic, thus having drastically di�erentmagnetic properties compared to SP. Picture in [Figure 2] shows a MPI image overlayed overa MRI image.

2 Magnetic particle imaging

2.1 Superparamagnetic particles respond to magnetic �eld

Superparamagnetic tracer is a suspension of many magnetic particles with a size of fewnanometers. A typical material used is iron oxide Fe2O3[Figure 3]. In bulk form, the materialis a ferromagnet known since ancient times, but when the size of particles decreases, they

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(a) Paramagneticnanoparticles can bemagnetized with apermanent magnet.[5]

(b) Microscopy imageof FeOx SP nanoparti-cles[5]

Figure 3: Macroscopic and microscopic images of superparamagnetic particles

start to behave as a single domain magnetic particle with a large magnetic moment thatcorresponds to the sum of several hundred individual moments. Typically, the magneticparticle size is 1−100 nm [6]. The nano particles are coated with a thick coating to separatethem and provide for good solubility.

If we subject these particles to an external magnetic �eld, their magnetic moments mi

start to align with it. We de�ne thermodynamic macroscopic magnetization as the sum ofall magnetic moments mi

M =1

∆V

N∑i=1

mi.

By considering large, i.e. nearly in�nite, magnetic moment that do not necessiate thequantum treatment and assuming the superparamagnetic particles are always in thermalequilibrium, their response to the magnetic �eld can be modelled using Langevin theory [7]

M = ρmL(x)H; x =H

H0

, H0 =kBT

µ0m. (1)

In this equation, ρ is density, de�ned as number of nanoparticles per volume, M is singlenanoparticle magnetization and L(H) is Langevin function, mathematically de�ned as

L(x) =

{coth(h)− 1

x; x 6= 0

0; x = 0.(2)

2.2 Detecting changes in magnetization

MPI explores the induced voltage in the receiver coils when SP magnetization changes withtime. Changes in magnetization can be detected by measuring the voltage induced bymagnetic �ux:

u(t) = − d

dt

∫S

B(r, t)dA. (3)

Here B is the magnetic �ux density that depends on the external magnetic �eld H andtime-dependent SP magnetization M(r, t).

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Figure 4: Magnetization of particles depends on the �eld applied. Region with high derivativeis highlighted.[5]

2.3 Spatial selection

The challenge is how to associate induced voltage with a particular point in space. If weput the object that contains magnetic SP in a magnetic gradient H(x) = Gx, where G is∂Hx

∂xgradient of magnetic �eld, we expose each particle to slightly di�erent magnetic �eld,

so di�erent points along the direction of �eld gradient will have di�erent thermodynamicmagnetizations according to Eq. (2). In the center (x=0), where magnetic �eld produced bygradient coils is zero, the SP are not magnetically satuated and will respond even to smallchanges in magnetic �eld. We will call this area �eld free point (FFP).

To detect particles in the FFP we apply another, oscillating �eld (extraction �eld). Dueto high derivative of the magnetization function M(H) around H = 0 [Figure 4], theseparticles will induce a signal with large amplitude and be easily detected. If the gradient�eld produced by the coils is strong enough, the FFP [Figure 5] will be very small. It isimportant to stress that all particles outside the �eld free point will be in the satuationregime and will thus produce no measurable signal.

A setup with a gradient "selection �eld" that determines the particles' response to smallchanges in the magnetic �eld, based on their spatial position and a weaker, oscillating "extraction �eld", suggests a simple imaging technique. We can place the object that is beingscanned in the selection �eld and move it around mechanically. With each move we canmeasure magnetization of particles in the FFP, until we scan the entire object. An exampleof a picture produced this way is seen in [Figure 6]. While the actual speed and accuracyheavily depend on mechanical implementation, it can take up to serval hours to scan avolume of a liter cube with a side long 1dm.

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Figure 5: Magnetic �eld inside a pair of Helmholtz coils[12]

Fortunately, there is a way to get around the drawbacks of this method. We can apply athird magnetic �eld, a drive �eld, that cancels out the selection �eld in a chosen direction,e�ectively moving the FFP instead of moving the object being scanned. This upgrademakes the process of imaging much faster and more accurate. Two examples of vector �elds,generated with this method, can be seen in [Figure 7].

2.3.1 Magnetic �elds

One of the options is generating all magnetic �elds with electromagnetic coils. A simplesolenoid coil can produce homogeneous �elds inside the coil if the coil is long enough. Makingthe coil too long results in high resistive losses and limits the scanner geometry. If wetake two shorter coils and separate them by a distance, the �eld between the coils will beapproximately homogeneous. Such setup is known as Helmholtz coils. A linear gradient�eld, such as the one needed for the selection �eld, can be generated by using a pair ofHelmholtz coils and inverting the current on one of the coils. This is sometimes refereed toas Maxwell coils. [Figure 8] displays a tipical one dimensional setup with two pairs of coils.

The superposition of the selection �eld, formulated as Gr and the drive �eld Hd can bewritten as

H = Hd(r, t)−Gr. (4)

By setting H(x, t) = 0, we can immediately calculate the location of the FFP xFFP from

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Figure 6: A picture taken by moving the object mechanically rather than using a drive�eld.[4]

this equation:xFFP (t) = G−1Hd.

Finally, we can write the equation of our magnetic �eld as

H(x, t) = G(xffp(t)− r).

The receiver coils pick up the sum of the voltage produced by the changes in magne-tization up and the voltage produced by the extraction and drive �elds uf . To get thesignal, resulted from the changes in magnetization, we need to subtract up(t) = u(t)− us(t).The voltage produced by changing magnetization is small compared to the extraction signal(typically, 6 orders of magnitude) [2].We will discuss this problem in chapter 3.1.

We have already calculated how magnetization changes with applied magnetic �eld:

up(t) = −µ0

∫ ∞−∞

p(r)∂M(G(xd(t)− r))

∂td3r. (5)

The factor p(r) takes is a correction that takes in account non ideal sensivity of the recievercoils. To avoid complex algebra, we will preform further calculations in one dimension,substituting M(r, t)→M(x, t).

The particle concentration only depends on the position, so it is sensible to split themagnetization function as M(x, t) = co(x)m(x, t).

Equation (5) can be written as a convolution:

up(t) = −µ0∂(Gxd(t))

∂tpx(c ∗m′(G(xd(t)− x))). (6)

The signal amplitude depends on the speed of the drive �eld, so to compensate for themovement, we need to divide our signal with the derivative of the drive �eld, obtaining

un(t) = −µ0px(c ∗m′)(G(xd(t)). (7)

2.4 Gridding

Our measurement is a time dependent signal un(t). To reconstruct a picture, we need toproject this signal onto a grid, or x-space. xd(t) determines the position of our free �eld

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Figure 7: Illustration of two possible positions of the free �eld point, depending on the drive�eld. On the upper picture, the x component of the drive �eld strength is greater than 0, onthe lower it is less than 0. Both vector �elds were plotted on an arbitrary scale to illustratea point[5]

point. This position depends on the choice of the drive �eld shape, which is usually chosenso it covers the space as uniformly as possible. A Cartesian trajectory (for our 1D modelxd ∝ (k∗t)) is the most obvious choice, but for imaging in two and three dimensions does notcover the space uniformly and other shapes are preferred. The [Figure 9] compares Cartesianand Lissajous trajectories in two dimensions.

3 Simpli�cations and limitations of the model

3.1 Filtering signals

In MPI imaging, the signal, produced by changes in SP magnetization is measured simulta-neously with the point selection determined by drive and extraction �elds. In section 3.2.1we have mentioned that these �elds produce a much stronger signal than the particles, so wecannot a priori �lter out these signals in digital post processing. Analog frequency �lteringcan remove signals, produced by drive and extraction �elds, but inevitably also removes basefrequencies of these �elds from the particle signal. It has been proven experimentally, thatthis only produces an o�set in the measured signal, that can be compensated for simply bydigitally forcing the signal to be positive[Figure 10].

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Figure 8: Picture of an example setup. The outer Maxwell pair of coils create the selection�eld whereas the inner coils create the weaker, extraction �eld.[4]

Figure 9: Comparison of Cartesian and Lissajous trajectories in two dimensions.[5]

3.2 Relaxation e�ects

Superparamagnetic nanoparticles have two stable, anti parallel orientations. Neel-Arrheniusequation determines the mean time (Neel time) τN between two �ips

τN = τ0 exp(KV

kbT). (8)

Here, K represents magnetic anisotropy energy, V volume of the nanoparticle, kb Boltz-mann constant, T temperature, τ0 material speci�c characteristic time. The product KVrepresents the magnitude of the energy barrier between the two orientations. If the mea-surement time τm is much longer than τN , the orientation of the particle will �ip many timesduring the measurement and in the absence of external �eld, the measured magnetization willequal 0. In this case the material is said to be in superparamagnetic state. The temperature,at which τm = τN can be expressed as:

TB =KV

kb ln(τm/τ0)(9)

and is called the blocking temperature. Typical values for iron oxide nanoparticles are around200 K, but depend heavily on particle size and temperature.

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Figure 10: The information lost by �ltered frequency presents as an o�set and is easilyrecoverable.[5]

In the model, described in this text we have neglected the time it takes for the particleto change magnetization orientation (adiabatic model). This is only true for small particleswith large magnetic moments. In [Figure 11], we can observe the di�erence between thetheoretical derivative of the Langevin theory in adiabatic approximation compared with thetheoretical model with relaxation correction and the experimental result. It has been shownthat the relaxation e�ect can be modelled with �rst order relaxation constant [source] andcan be adjusted by designing di�erent nanoparticles. Simply making nanoparticles smalleris not enough, because smaller nanoparticles have lower magnetic moments. As a rule ofthumb it is good to have particles with large core and thin coating.

The particles also rotate due to Brownian rotational di�usion[7] with characteristic timeτB

τB =3V η

kBT. (10)

Unlike Neel relaxation, rotational di�usion characteristic time is slower than the �eld switch-ing and has little in�uence on MPI.

3.3 Scaning volume

One of the most important performance characteristics for a scanner to be useful in medicineand other �elds is maximum size of the scanned volume, which is determined by the strengthsof the selection and drive �elds. At typical drive frequencies (≈ 25 kHz), it is not possi-ble to use magnetic �eld strength larger than 20 mT/µ0, because they heat the patienttoo much. With these �eld strengths, it is di�cult to scan areas with volume larger than16mmx25mmx25mm. As a workaround, we can introduce another �eld, called focus �eld,that operates at a much lower frequency and shifts entire scanning area. Because of the dia-magnetic nature of human body, the magnetic �elds do not get absorbed and can penetratethe entire scanning volume.

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Figure 11: Relaxation e�ects on the derivative of the Langevin function. [2]

4 Summary

Magnetic particle imaging is a very promising technique with great potential for research andclinical use. On the research side, there are many groups developing new superparamagneticnanoparticles, scanner designs and image reconstruction techniques. At the time of writing,there are no known limitations that would prevent us from building a safe, fast, full bodymedical scanner, but such scanner does not exist yet. It is expected that the method will beespecially well adopted in angiography.

References

[1] William R. Hendee, E. Russel RitenourMedical Imaging Physics, A JOHN WILEY &SONS, INC., PUBLICATION, 2002

[2] Dr. P. W. Goodwill , Dr. E. U. Saritas , L. R. Croft , T. N Kim : X-Space MPI: Magnetic

Nanoparticles for Safe Medical Imaging, University of California,

[3] Gleich, B.: Verfahren zur Ermittlung der r�aumlichen Verteilung magnetischer Partikel.German Paten

[4] Bernhard Gleich, Jurgen Weizenecker: Tomographic imaging using the nonlinear re-

sponse of magnetic particles, Vol 435|30 June 2005|doi:10.1038, nature03808

[5] Patrick W. Goodwill and Steven M. Conolly : The X-Space Formulation of the Magnetic

Particle Imaging Process: 1-D Signal, Resolution, Bandwidth, IEEE TRANSACTIONSON MEDICAL IMAGING, VOL. 29, NO. 11, NOVEMBER 2010

[6] Hamed Arami, R. M. Ferguson, Amit P. Khandhar, and Kannan M. Krishnan: Size-

dependent ferrohydrodynamic relaxometry of magnetic particle imaging tracers in dif-

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ferent environments, Department of Materials Science and Engineering, University ofWashington, P.O. Box 352120, Seattle, Washington 98195-2120

[7] Ilsu ree : Superparamagnetic Transition in Ultrasmall Superparamagnetic Iron Oxide

Nanoparticles, Depeartment of Physics, Kyungpook Natipnal university, Daegu 702-701, 16.1.2007

[8] Tobias Knopp. Thorsten M. Buzug: Magnetic Particle Imaging - An Introduction to

Imaging Principles and Scanner Instrumentation, Springer-Verlag Berlin Heidelberg2012, ISBN 978-3-642-04199-0 (eBook)

[9] J. Weizenecker, B. Gleich, J. Rahmer, H. Dahnke and J. Borgert : Three-dimensionalreal-time in vivo magnetic particle imaging, Hamburg, Sector Medical Imaging Systems,Rontgenstrasse 24-26, 22335 Hamburg, Germany

[10] B. Gleich, J. Weizenecker, H. Timminger, C. Bontus, I. Schmale, J. Rahmer, J. Schmidt,J. Kanzenbach, and J. Borgert : Fast MPI Demonstrator with Enlarged Field of View,Philips Technologie GmbH, Forschungslaboratorien, Hamburg, Germany

[11] Patrick W. Goodwill and Steven M. Conolly : Multidimensional X-Space Magnetic

Particle Imaging, IEEE TRANSACTIONS ON MEDICAL IMAGING, VOL. 30, NO.9, SEPTEMBER 2011

[12] Patrick W. Goodwill, Steven M. Conolly : Multidimensional X-Space Magnetic Particle

Imaging, Hamburg, IEEE Trans Med Imaging. 2011 September ; 30(9): 1581�1590.doi:10.1109/TMI.2011.2125982

[13] Tobias Knopp, Thorsten M. Buzug: An Introduction to Imaging Principles and Scanner

Instrumentation, ISBN 978-3-642-04199-0 (eBook)

[14] Spletna stran http://en.wikipedia.org/wiki/Superparamagnetism

[15] Spletna stran http://en.wikipedia.org/wiki/Nèel_relaxation_theory

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