MPS and ACS with an Atomic Magnetometer

International Journal on Magnetic Particle Imaging

MPS and ACS with an atomic magnetometer

Simone Colomboa, Victor Lebedeva Zoran D. Grujića Vladimir Dolgovskiya Antoine Weisa ∗ · · · · a Département de Physique, Université de Fribourg, Chemin du Musée 3, 1700 Fribourg, Switzerland Corresponding author, email: [email protected] ∗

Abstract We show that a single atomic magnetometer in a magnetically unshielded environment can be used to perform magnetic particle spectroscopy (MPS) and AC susceptometry (ACS) on liquid-suspended magnetic nanoparticles. We demonstrate methods allowing a simultaneous recording of M (H) and dM /dH(H) dependences of samples containing down to 1 µg of iron. Our results pave the way towards an atomic magnetometer based MPI scanner.

I. Introduction cally pumped atomic magnetometer (OPM), and demonstrate that an OPM can be used for Magnetic Particle The technique of Magnetic Particle Imaging (MPI), fol- Spectroscopy (MPS) and AC susceptometry (ACS). MPS is often referred to as zero-dimensional MPI, and any high- lowing its introduction in 2005 [1], has evolved along sensitivity MPS method is thus a necessary prerequisite two major pathways, viz., frequency-space MPI [2] for developing an MPI system. and X-space MPI [3], both approaches having their respective merits and drawbacks. MPI relies on ex- Laser-driven OPMs are compact and versatile instru- citing a magnetic nanoparticle (MNP) sample by a ments, mostly operating at room temperature, that can monochromatically oscillating (frequency f scan) drive detect magnetic field changes in the femto- or even sub- field Hscan(t )—referred to as ‘scan’ field in this paper— femto-Tesla range. Recent review of various OPM prin- and detecting the polychromatic time-dependent mag- ciples and their applications is given in Ref. [6]. In netic induction BNP(t ) M NP that arises as a conse- the past decade OPMs have been deployed for biomag- ∝ quence of the nonlinear M NP(Hscan) relation. Most MPI netism studies, such as magnetocardiography [7, 8] and approaches developed so far share the common fea- magnetoencephalography [9]. The suitability of OPMs ture that the detected signal SNP(t ) is recorded by in- for studying the magnetorelaxation of blocked MNPs was duction coil(s). Because of Faraday’s induction law, one demonstrated in recent years [10, 11, 12]. More recently has SNP d BNP(t )/d t d M NP(t )/d t n f scan, where n de- we have shown (Ref. [13] in this volume) that OPMs can notes the∝ order of the∝ detected overtones,∝ so that sig- also be used for the quantitative measurement of the sat- nal/noise considerations call for large drive frequencies. uration magnetization, MS , the iron content and particle A high-frequency drive favors high speed operation per- size distributions of aqueous MNP suspensions. We be- mitting fast volumetric scans of the sample [4]. lieve that because of their high sensitivity and large bandwidth (DC up to hundreds of kHz), OPMs, when com- Frequency-domain operation profits from S/N ratio enhancement by selective bandpass-filtering of the har- bined with a variant of X-space MPI, have the potential monics at known frequencies, but involves demanding to yield a complementary, low-frequency MPI technique. calibration procedures. X-space MPI, on the other hand, allows a simpler interpretation of the recorded (filtered) time series, leading to a computationally less demanding II. Experimental apparatus image reconstruction based on the a priori known field arXiv:1612.07094v1 [physics.bio-ph] 21 Dec 2016 free point (or line) position. Both methods suffer from a The main components of the apparatus (mounted in direct strong drive field contribution to the detected in- a walk-in size double-layer aluminium chamber) are duction. From the point of view of applying MPI to bio- sketched in Figure 1. The MNP sample is excited by a logical systems, in particular to humans, unwanted neu- periodically oscillating scan field Hscan(t ) produced by a ral stimulation and unwanted side effects from excessive 700 mm long, 14 mm diameter solenoid, next to which SAR (specific absorption rate) become pronounced at el- an identical, but oppositely poled solenoid reduces resid- evated frequencies and/or drive coil power [5]. ual field at the OPM location ( 7 cm above the two Here we report on the detection of the anharmonic solenoids) to 1 nT per mT of scan∼ field (more details magnetic response of MNPs by a high sensitivity opti- are given in [13∼]).

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The HF2LI lock-in ampliﬁer delivers a voltage dM(H)/dH FT M’(n f) f f + frf (t) m ref ~ Sδf (t ) = αδf NP(t ), which allows retrieving the corre- S f- f+ FM + LIA in sponding detected induction change (Fig. 1).

in frf (t) SAM - LIA III.I. Magnetization curve M (H) f ref optical - laser Similarly to the method described in [13] we ex- fiber F 50 Hz VCO cite the sample by a field Hscan(t ) of amplitude Cs cell ∼ PD I/U PLL 15 mTpp /µ0 that sinusoidally oscillates at a frequency f scan of 600 mHz. We record time series (sampled at a rate of 320 S s) of I t and the induced signals d / scan( ) B0 BNP f (t) rf δBNP(t )=Sδf (t )/(αγF ). These time-space results are laser shown as the lower two traces of Fig. 2. The recording was rf coils beam MNP sample M(H(t)) done on a 500 µl EMG 707 sample containing 3.4 mg of drive FT iron (more details on the− sample given in [13]). d Iscan (t)+ Im (t) compensation M(n f) 833 ms dBNPdHscan Figure 1: Sketch of the experimental setup. LIA: lock-in amplifier; PD: photodiode; I/U: transimpedance amplifier; VCO: voltage-controlled oscillator. f refers to frequencies f r f f m . ± ± 50 nT BNP

The OPM is based on optically detected magnetic res- Hscan 7.5 mTΜ0 onance in spin-polarized Cs vapor [7]. The sensor is op- time erated in a homogeneous bias magnetic field B0 of 27 µT, produced by large ( 3 3 3 m3) Helmholtz coils, which Figure 2: From bottom to top: Time series of the scan also cancel the local∼ laboratory× × field. We note that the field Hscan(t ), the corresponding induced δBNP(t ) M NP(t ), and MNP sample is also exposed to that bias field. The Cs ∝ dBNP/dHscan(t ) dM NP/dHscan(t ) dependencies. The scan fre- spin polarization in the sensor precesses with a Larmor quency was 600∝ mHz and the data shown are unfiltered raw frequency f prec of 95 kHz in that field. The precession is data containing 533 data points per period. driven phase-coherently by a weak (few nT) field oscillating at the ‘rf’ frequency f rf generated by a low band- Performing the Fourier transform of data from 30 con- width ( 50 Hz) phase-locked loop (PLL, Fig. 1) ensuring ∼ secutive scan cycles yields the harmonics spectrum that the magnetic resonance condition f rf=f prec is main- tained when f , i.e., B~ varies. The driven Cs spin pre- prec 0 Sδf (t ) B f /f δB t (2) cession impresses a modulation| | (at f rf) on the detected eNP( scan) = [ NP( )] = F F αγF light power. The B0 field information is thus encoded in that can be rescaled to magnetization units by terms of the frequency f rf=γF B~ 0 , where γF 3.5 Hz/nT for Cs. | | ≈ 4πR3 M NP = BeNP , (3) µ0Vs

III. Measurements and results where Vs is the sample volume and R the sample- magnetometer spacing (7 cm).The top graph of Fig. 3 Small MNP-induced field changes δB~ NP(t ) B~ 0 in the shows such a Fourier spectrum. When rescaled to unity | || | total field at the sensor position B~ tot(t ) yield correspond- bandwidth, the noise floor in the figure represent a ing OPM frequency changes power spectral density of 4 pT/pHz which limits the detectable number of harmonics∼ in the M (H) signals to ~ ~ δf NP(t ) = f (t ) f 0 = γF Btot(t ) B0 23 for 3.4 mg of iron. The noise pedestal underly- − | | − | | ≈ = γF δB~ NP(t ) Bˆ0 . (1) ing the low-frequency Fourier components reflects low- · frequency noise and drifts of the magnetic field at the To first order in δBNP the OPM signal is thus determined sensor location. We draw attention to the fact that, con- by the projection δBNP(t ) B~ NP(t ) Bˆ0 of the field of inter- versely to conventional MPS methods, our technique est onto the bias field, making≡ the· OPM an effective vec- gives also access to the fundamental frequency of the tor component magnetometer. The sensitivity to MNP MNPs’ magnetic response. In relation to the latter state- signals will be maximized by having B~ 0 δB~ NP. ment we also note that here we derive the harmonics k http://dx.doi.org/ijmpi.xxxx.xxxxx 2 International Journal on Magnetic Particle Imaging

n=1 ple’s saturation field, the harmonic amplitudes mn 1 are 104 > n=3 negligible, and the first harmonic reduces to 103 L d M H t rms 2 NP [ scan( 0)] 10 m1 t0 δHm δHm M Hscan t0 . pT ( ) = NP0 [ ( )] H d H ≡ NP 101 (6) B At each time t0, the magnetization component oscillating 100 at f m is thus proportional to the derivative of the MNPs’ 10-1 M (H) dependence (Langevin function). 102 n=2 We extract a signal proportional to m1 (Hscan(t0)) in n=4 the following way: The sample’s magnetization com- 1 10 ponent m0 (varying at the slow frequency f scan) and L the sample’s magnetization component m1 (oscillating a.u. H 100 at f m) produce magnetic induction fields BNP(t0) and AC Χ δBNP(t0)cos (2πf mt ), respectively, that add to the offset 10-1 field B0 at the sensor location. The magnetometer signal is a photocurrent oscillat- 10-2 ing at a frequency proportional to the modulus of the to- -30 -25 -20 -15 -10 -5 0 5 10 15 20 25 30 tal induction field n=f fscan

Figure 3: Fourier transforms of 30 cycles ( 50 s recording time) Btot(t )=B0+BNP(t0)+δBNP cos(2πf mt ), (7) ∼ of BNP(t ) and dM /dH(t ) data as shown in Fig. 2. Top: Magnetic particle spectrum (MPS). Bottom: Fourier spectrum of AC sus- where BNP B0 . One sees that the problem of infer- | || | ceptibility. ring the amplitude of the m1(t ) component is a problem of FM spectroscopy. The corresponding time-dependent photodiode signal is given by spectrum of M f /f from a direct measurement of fNP( scan) M H t , while conventional MPS (and MPI) devices f p NP ( ( )) UPD t A t cos 2πf rf t sin 2πf mt , (8) ( ) = ( ) + f do the opposite, i.e., reconstruct M NP(H) from recorded m MfNP(f /f scan) values. where f p =γF δHm. Since the PLL is tracking slow varia- tions BNP of B0 field, we have omitted, in Eq. 8, the con- III.II. AC susceptibility =dM /dH χAC tribution γF BNP(f scant0) to f rf=γF B0. We extract the side- We have extended the method discussed above for mea- band amplitudes by the sideband demodulation technique illustrated in Fig. 1, which thus gives simultaneous suring M (H) curves towards the direct and simultaneous access to both d M /d H H and M H . recording of the derivative, i.e., dM /dH(H)-dependence. ( ) ( ) For this we excite the sample with a bichromatic super- The top trace of Fig. 2 shows the derivative signal position of fields dBNP/dHscan(t ), which—after calibration by Eq. 3—is equivalent to d M NP/d H. The Fourier spectrum of 30 cy- bi Hscan(t ) = Hscan cos 2πf scant + δHm cos 2πf mt , (4) cles of dBNP/dHscan(t ) data is shown as lower graph in Fig. 3. Comparison of the two Fourier spectra reveals with a scan field of amplitude Hscan 15 mTpp /µ0 and the superior power of FM-spectroscopy: While the di- a weaker modulation field δH <2 mT∼ /µ . The quasi- m pp 0 rect M (H) method is sensitive to drift and low frequency static scan at frequency f scan 1 Hz f m 753 Hz im- = = noise of the ‘background’ field B0 at the sensor (as evi- plies that at any given time t0, the MNPs’ magnetization P denced by the noise pedestal under the upper spectrum is given by M NP t0 mn t0 cos n 2πf mt , where ( )= n=0 ( ) ( ) in Fig. 3), the derivative spectrum is insensitive to low- m0 M NP [Hscan(t0)], and where frequency changes of the carrier frequency f . ≡ rf 1 While the BNP f spectrum is dominated by odd f mt0+ 2 e ( ) Z Fourier components, even frequency components domi- bi mn>0(t0)=4 M NP Hscan(t ) cos(n2πf mt )d(f mt ) nate the dB t f t NP( ) m 0 χeAC (f ) (9) 1 ∝ F dH 2 H Z δ m bi p 2 spectrum. = M NP0 Hscan(t0;x) 1 x Un 1(x)dx . (5) nπ − − The Fourier spectra show some artifacts. The up- 1 − per graph of Fig. 3 contains a series of even harmonics ~ In the last expression Uj is the j th Chebyshev polyno- arising from field components δB (t ) perpendicular to − p ⊥2 2 mial of the second kind. For δHm

contains terms oscillating at even harmonics, the domi- Acknowledgements. This work was supported by nant one being at 2f scan. In the lower graph of Fig. 3 the Grant No. 200021_149542 from the Swiss National Sci- odd harmonics are mainly due to the fact that Hscan does ence Foundation. not oscillate around zero, but rather around the average value Hscan =B0/µ0 of 27 µT/µ0 (bias field). In〈 a series〉 of dilution experiments we have demonstrated the proportional scaling of the M (H) [13] and References dM /dH signals with iron content. Based on the lower graph of Fig. 3 that was recorded with 3.4 mg of iron, we estimate that our current detection limit in a recording [1] B. Gleich and J. Weizenecker. Tomographic imaging using the time of 50 s is 700 ng of iron. nonlinear response of magnetic particles. Nature, 435:1214–1217, ∼ 2005. doi: 10.1038/nature03808. [2] N. Panagiotopoulos, R. L. Duschka, M. Ahlborg, G. Bringout, Ch. Debbeler, M. Graeser, Ch. Kaethner, K. Lüdtke-Buzug, H. 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