Journal of Low Temperature Physics - QFS2009 manuscript No.(will be inserted by the editor)

Development of MRI Microscope

Mahiro Hachiya ´ Kyohei Arimura ´Tomohiro Ueno ´ Akira Matsubara

Received: date / Accepted: date

Abstract We have been developing an ultra high spatial resolution MRI, “MRI

Microscope”, especially for 3He physics at ultra low temperature. The ultimate goal

of our MRI Microscope is to achieve 1 µm × 1 µm two dimensional spatial resolution

comparable to optical microscopes. We constructed the MRI Microscope using mag-

netic field of 7.2 T, tri-axial magnetic field gradients of 2.0 T/m. We visualized the pure

liquid 3He in 230 µm diameter tube to study nonlinear effect on the MRI Microscope

in high magnetic fields and at low temperature. The MRI image was obtained at 0.22

MPa, 1 K with 1.8 µm × 1.8 µm pixel size. At 65 mK, the MRI image became more

blurred. We speculate that it was caused by larger spin diffusion and nonlinearity.

Keywords Helium-3 · MRI · MSE

PACS 76.60.Pc · 67.30.E- · 67.30.er

1 Introduction

The Magnetic Resonance Imaging, “MRI”, becomes an essential tool for clinical di-

agnosis due to its ability to distinguish biological tissues. This ability is originated from

the rich nature of NMR. In low temperature physics, NMR has revealed many inter-

esting phenomena. We developed MRI for ultra low temperature physics, “ULT-MRI”,

to visualize spatially inhomogeneous magnetic properties, especially of 3He.[1] By us-

ing ULT-MRI, phase-separated 3He-4He mixtures and magnetic domain structures in

M. HachiyaGraduate School of Science, Kyoto University, Kyoto 606-8502, JapanE-mail: hachiya@scphys.kyoto-u.ac.jp

K. ArimuraGraduate School of Science, Kyoto University, Kyoto 606-8502, Japan

T. UenoGraduate School of Medicine, Kyoto University, Kyoto 606-8507, Japan

A. MatsubaraResearch Center for Low Temperature and Materials Sciences, Kyoto University,Kyoto 606-8502, Japan

2

the U2D2 phases of solid 3He were visualized.[2][3] In these images, however, the two

dimensional spatial resolution was limited to 25 µm × 25 µm even in the best case

(3He-4He mixture).

In order to make more precise measurements of MRI possible, we have been develop-

ing ULT-MRI with an ultra high spatial resolution, “MRI Microscope”, by exploiting

low temperature and high magnetic field environments. The ultimate goal of our MRI

Microscope is to achieve 1 µm × 1 µm 2D resolution. The resolution of MRI, ∆x, is

expressed as

∆x =2π · ∆f

γG(1)

where ∆f is minimum detectable frequency difference, γ is gyromagnetic ratio and

G is magnetic field gradient strength. In order to obtain higher spatial resolution,

stronger magnetic field gradient is necessary. To maintain image quality in a high-

resolved picture, we should increase signal to noise ratio (S/N) accordingly. When

noise from the resonance circuit itself is dominant, S/N increases with magnetic field,

H, as S/N ∝ H74 .[4] In the paramagnetic system, magnetization, M , follows Curie

law, S/N ∝ M ∝ 1T , where T is temperature. We could improve drastically the spatial

resolution at low temperature and in higher magnetic fields. This is our approach of

MRI Microscope.

Different limitation, however, may be posed on this brute-force type approach, when

we treat 3He system. Due to Fermi liquid property of liquid 3He, spin diffusion coeffi-

cient, Ds, increases as Ds ∝ 1T 2 and magnetic susceptibility, χ, becomes temperature

independent at low temperature. Large dipole field in high magnetic field produces

multiple spin echo (MSE).[5] At low temperature and in high magnetic field, the

Leggett-Rice effect shows up and generate spin wave.[6] In this report, we consider

spin diffusion, MSE effects and show preliminary images of the MRI Microscope at 1

K and 65 mK. We disscuss the differences between two images.

2 Nonlinear Effect

If GL ≪ H, where L is a sample size, Bloch equation with spin diffusion can be

linearized and spin-echo height can be expressed as

S(τ) = S(0) exp(− 1

12γ2G2Dsτ

3)

(2)

where τ is a pulse interval between first excitation pulse and second excitation pulse.

When we apply π/2 - π pulse sequence in order to maximize S/N, as ordinary MRI,

large spin diffusion strongly dump the signal intensity at low temperature with strong

magnetic field gradient. Since large G is necessary for higher spatial resolution even

with large spin diffusion[7] , shorter pulse interval is required so as to suppress signal

intensity dumping.

However, the shorter pulse interval causes a new problem that spin-echo has larger

overlapping with FID of second pulse (2nd FID). 2nd FID is mainly caused by inho-

mogeneity of RF field in frequency domain and in real space, and does not respond

to magnetic field gradient linearly. Quadrature phase-shift keying (QPSK) technique

was employed to eliminate 2nd FID.[8] FID of 1st excitation pulse (1st FID) also can

be canceled by the QPSK. We found that 1st FID had little or no influence for MRI

3

Fig. 1 (A) Sample Cell: (1) NMR Zone (2) Gradient Coils (3) Main Magnet (4) Capacitors(5) Sample Inlet (6) Sintered Silver (7) Copper Spacer (B) NMR Zone: (1) Transmitter Coil(2) Receiver Coil (3) Polyimide Tube

images in our case, we performed only 180◦ phase change for 2nd pulse.

At low temperature and in high magnetic field, large magnetization generates large

dipole field. When we apply π/2 - π/2 pulse sequence under magnetic field gradient,

the spatially modulated longitudinal magnetization induces MSE.[5] The MSE causes

wave pattern in MRI spectra. The MSE does not appear by applying π/2 - π pulse

sequence, since there is no spatial modulation in longitudinal magnetization after the

π pulse. In the experimental situation, tipping angle is not same over the sample space

and frequency space. The real π pulse spatially modulates longtudinal magnetization,

and then MSE appears. High homogeneity of RF magnetic field both in frequency

domain and visualization area is required to eliminate the above MSE effect. Larger

diameter coil for spatial homogeneity and hard pulse for the homogeneity in the fre-

quency domain are necessary. We used the cross-coil configuration and larger diameter

transmitter coil. We improve Q-value of resonanse circuit of the transmitter coil in

order to shorten pulse width.

3 Experimental Setup

We used the usual π/2-π pulse echo method for NMR detection. Fig. 1 (A) shows the

experimental configuration, and the closeup of the NMR region is displayed in Fig. 1

(B). The static field H0 for NMR was vertical (along z-axis) and 7.2 T in magnitude.

The direction of the polyimide tube, which we call x-axis, was aligned in the horizontal

plane. y-axis was determined to construct a triade with x and z-axes. Tri-axial mag-

netic field gradients of 2.0 T/m were applied for MRI imaging. Spatial resolution in

calculation is 1.2 µm × 1.2 µm.

The pure 3He sample in 230 µm inner diameter polyimide tube was visualized at

1 K and 65 mK, which was cooled with a dilution refrigerator (DR). 80 µm diameter

Cu wire was wound every other turn for a receiver coil for higher homogeneity.[9] The

receiver coil was located just out side of the polyimide tude of 300 µm outer diameter

4

Fig. 2 MRI images of Liquid 3He in the 230 µm ID tube at 0.22 MPa; (A) at 1 K with G= 1.3 T/m, (B) at 65 mK with G = 0.87 T/m. Axes in the images correspond to the axes inFig. 1.

and 1 mm long. A Helmholtz coil of 5 mm diameter and 2.5 mm gap was used as a

transmitter coil, whose homogeneity is calculated to be 99.99 % in the visualization

region. The transmitter coil was aligned with y-axis, which was perpendicular to both

H0 and the polyimide tude direction.

For the resonance circuit nonmagnetic variable capacitors were used, which posi-

tioned 1 cm blow the receiver and transmitter coils. Compact tank circuit in the low

temperature region could improve Q-value to 90 for the receiver and 80 for the transmit-

ter coils. With large Q-value the pulse width could be shortened, and the homogeneity

of RF-field in frequency domain became more than 99 %. The resonance circuit for the

receiver coil was thermally anchored to the mixing chamber of DR and anchored to

the 1 K stage for the tranmitter coil.

The process to get the MRI figure was similar to the reference [1], other than QPSK

technique. Pulse interval was 500 µs, which we determined exprimentally, and pulse

width of the π/2 and π-pulses were 0.6 µs and 1.2 µs, respectively.

4 Results and Discussions

We visualized liquid 3He at 0.22 MPa, 1 K and 65 mK. Only the tube image regions

are displayed (250×250) of obtained images (1024×1024) are shown in Fig. 2 (A), (B),

respectively. In Fig. 2 (A), we could apply 1.3 T/m of magnetic field gradients, and in

Fig. 2 (B), 0.87 T/m due to quench problem of the superconducting graient coils. As

a result, the pixel size became 1.8 µm × 1.8 µm in Fig. 2 (A) and 2.7 µm × 2.7 µm in

Fig. 2 (B). The diameters of tube images were different due to the pixel size difference.

Since normal liquid 3He had no structure, we expected the simple circle images. In

both of Fig. 2 (A), (B), however, a crest-moon-like artifact existed around the lower

part of the tube image. At closer look, relative position of the artifact in the tube

changed with temperature. We could see wave pattern in Fig. 2 (B) more clearly. The

simple spin diffusion could not explain the artifact and the image differences.

We took fourier transforms (FT) of the original images of Fig. 2 (A), (B) (matrix size

1024×1024) and showed in Fig. 3 (A), (B), respectively. We could approximate that

FT images corresponded to time domain signals distributed in the k-space according

5

Fig. 3 Fourier transformed MRI images of Fig. 2; (A) at 1 K, (B) at 65 mK. Image matrix is1024×1024.

to magnetic field gradient direction even after the signal procession described in Sec. 3.

In both FT images of Fig. 3, fan-type signal spreads existed in the range from 0◦ to

45◦ and from 135◦ to 180◦. (the angle was measured from the ky axis) This means

that when we applied the magnetic field gradient along the direction in the above

angle range, the spin-echo signals continued longer in time than those did under the

gradient along the difference direction. If small impurity, such as ferromagnets existed,

the strength of the gradient might change with its direction. We compared spectrum

width, which coresponded to the sample size, between the spin-echo signals in the range

and those out of the range. We found that the spectrum width was same in the all

angle range. Since our signal sampling time was order of T2, we speculated that the

nonlinear effects, such as MSE, spin flow[10], spectral clustering[11] might causes the

fan-type signal spread.

Before we discussed further, we considered the temperature difference in Fig. 2. We

calculated the spin diffusion effect.[12] At 1 K and at 65 mK,

D1K = 6.81 × 10−5cm2/s, b1K = −3.98 × 107τ3/s3 (3)

D65mK = 24.83 × 10−5cm2/s, b65mK = −6.50 × 107τ3/s3 (4)

where b = − 112γ2G2Dτ3.(Eq. 2) Even though G1K was stronger than G65mK , the

difference in Ds produced the situation where the diffusion effect at 1 K was smaller

than that at 65 mK. (exp(b65mK) < exp(b1K)) Therefore, the spin-echo signal should

decay faster at 65 mK than at 1 K. However, the spin-echo signals continued longer at

65 mK than at 1 K.

One of possible causes is MSE. We found MSEs at 1 K and 65 mK although we

applied π/2 - π pulse sequence. The spin-echo signal amplitudes under the gradient of

the angle 135◦ at 1 K, 65 mK were shown in Fig. 4 (A), (B), respectively. We showed

simulated spin-echo amplitude without nonlinear effects as broken lines in Fig. 4. As

indicated as the arrows in Fig. 4, MSE at 65 mK was larger than at 1 K. These

MSEs under the π/2 - π pulse sequence was caused by the RF field inhomogeneity.

One possible causes of the RF inhomogeneity was mechanical imperfection such that

the relative position of the transmitter coil pair was different from the caluclation.

Another possiblity was the tipping angle dependent frequency shift under large dipole

field.[13] According to culculations without spin diffusion effects, however, MSE has

6

Fig. 4 Collected spin-echo signals under the gradient of the angle 135◦ abd simulated signalswithout nonliner effects; (A) at 1 K, (B) at 65 mK. The arrows indicate possible positions ofMSEs.

no gradient direction dependent execept for the phase. In our cases, large spin diffusion

existed. MSE with large spin diffusion[14] and other nonlinear effects may explain the

experiments. Further calculations and simulations are in progress.[15]

Acknowledgements We would like to thank Prof. Mizusaki for stimulating disscussions andto appreciate for commitments of Ms. Chen, Mr. Ogawa, Prof. Sasaki in the early stage of thiswork. This research was partially supported by Grants-in-Aid from Japan Space Forum, JapanSociety for the Promotion of Science and Ministry of Education, Culture, Sports, Science andTechnology of Japnan.

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