Introduction

Magnetic resonance imaging (MRI) systems are widely used for clinical diagnostics and are typically performed in a high magnetic field from 1.5 T to 7 T. High fields are preferred to achieve sufficient signal required for short imaging times (less than a few minutes) and high spatial resolution (less than a millimeter). Contrast agents are widely used in clinical MRI, to enhance image contrast by either increasing (positive contrast)1 or decreasing (negative contrast)2,3,4 the local magnetic resonance (MR) signal. This is typically done by locally reducing T1 or T2, for positive and negative contrast respectively, where T1 is the longitudinal and T2 is the transverse proton spin relaxation time. T1 relaxation comes from the fluctuating electron spin moment of the contrast agent coupling with neighboring water protons inducing energy transfer5. The proton spins that are very near the contrast agent quickly relax back to their equilibrium magnetization, leading to a shortened T1 and an enhanced MR signal since the proton magnetization fully recovers between excitation pulses. In contrast, T2 relaxation comes from long-range magnetic dipolar fields of the magnetic particles that shift the proton resonance frequency locally and dephase the proton spin precession, leading to a short T2 and a reduced MR signal5. In this letter we show that magnetic nanoparticles, which give large negative contrast in high field MRI, give very large positive contrast in ultra-low field (ULF) MRI and demonstrate that, by tailoring the magnetic nanoparticle fluctuation rate, agents with much higher visibility can be obtained.

Superparamagnetic iron oxide nanoparticles (SPIONs) have enhanced magnetic moment, typically by a factor of ~1000, compared to conventional Gd-based paramagnetic agents, leading to large relaxation effects6,7,8. At clinical MRI fields (1.5 T or 3 T), T1 reduction for SPIONs is small since magnetic fluctuations are suppressed while T2 reduction is large due to the nearly saturated time-average moment of SPIONs and the large local volume over which water protons are dephased2,3,4. SPIONs with negative contrast have been used for detection of hepatocellular carcinoma9,10, prostate cancer11, sentinel lymph node localization in breast cancer12, diagnosis of cardiovascular disease13, identifying inflamed carotid plaques14,15 and cell tracking16. Even though T2 suppression of SPIONs can improve the imaging contrast by reducing the MR signal, T1 agents are preferred since they enhance signal, preserve the underlying tissue signal, and shorten the imaging times. T1 contrast enhancement has been reported at high magnetic fields for certain SPIONs17,18,19,20 including ultra-small-size Fe3O4 nanoparticles (<3 nm)18, Gd doped Fe3O4 nanoparticles (4.8 nm)19 and Fe3O4 nanoplates20. In some cases the relaxation is believed to be due to surface-spin canting effects.

Here, we present an alternative approach for achieving T1 contrast enhancement from SPIONs by going to ultra-low magnetic fields. In ULF MRI systems, the operating magnetic field B0 is around 0.13 mT, corresponding to a resonance frequency of f0 = 5.56 kHz, which is four orders of magnitude lower than a typical clinical MRI field of 1.5 T (f0 = 63.87 MHz)21,22,23,24,25. At ultra-low field, the magnetic moment of the SPIONs is not saturated, and they have large spin fluctuations. T1 (positive) contrast can be greatly enhanced since the proton Larmor precession period is comparable with the relaxation times of magnetic nanoparticles26,27,28,29, leading to a large increase in the proton spin longitudinal relaxivity r1. The proton spin relaxivities, r1 and r2, are the change in relaxation rates R1 and R2 per unit Fe concentration, respectively, where R1 = 1/T1, R2 = 1/T2. In addition, the smaller non-saturated magnetic moment of the nanoparticle reduces the transverse relaxivity, r2, compared to the high field r2, minimizing undesirable negative contrast.

Results

Magnetic resonance measurements

MR measurements were performed in a low-cost ULF MRI system with a Faraday coil detector and a bilateral planar coil array that includes the B0 coil and the gradient field (Gx, Gy and Gz) coils. The earth’s field was cancelled by two pairs of Helmholtz coils (Bx and By), as shown in Fig. 1(a). To generate a measurable signal for the ULF MRI scanner, a pre-polarization field pulse (34.5 mT) is applied to enhance the proton magnetization before the MR pulse sequence. For imaging, we used a typical T1-weighted ULF MRI gradient echo (GRE) pulse sequence with repetition time (TR) of 400 ms, and gradient echo time (TE) of 27 ms as shown in Fig. 1(b). Five types of SPION solutions were used: 11 nm Fe3O4 and 16 nm Fe3O4 nanoparticles with citric acid surface modification, and 18 nm Fe3O4@SiO2, 22 nm Fe3O4@SiO2 and 18 nm Zn0.3Fe2.7O4@SiO2 nanoparticles with a thin shell surface coating of SiO2. The dimensions listed are the average core diameter. The synthesis processes along with transmission electron microscopy images are described in the Methods section and in references30,31,32. SPIONs were diluted with deionized (DI) water and transferred to 16 mL sample vials for ULF MRI imaging. The particle concentrations range from 0.25 µg/mL to 40 µg/mL by weight corresponding to Fe concentrations ranging from 0.00325 mM to 0.52 mM. A photograph of a sample vial with SPION solution is shown in Fig. 1(c). T1-weighted ULF MRI 2D GRE images are obtained with a pixel size of 2.8 mm × 3.6 mm with imaging duration of 1.6 hours, which is slower than that of superconducting quantum interference device (SQUID) detected ULF MRI (due to our lower signal to noise ratio) but sufficiently fast enough for the study here. The ULF MRI showed significant differences among five types of SPION solutions in Fig. 2(a–e). The ULF MRI signal versus Fe concentration for each SPION solutions are plotted in Fig. 3(a) (with the signal normalized to the DI water signal set to an arbitrary intensity of 1000). The ULF MRI signal initially increases (positive contrast) with increasing Fe concentration, at very low Fe concentration, due to the suppression of T1, while at high Fe concentration the signal decreases (negative contrast) due to shorter T2 times. This leads to a peak in the signal vs. Fe concentration; similar phenomenon has been observed in regular Gd-based T1 contrast agents33. To achieve the same T1-weighted ULF MRI signal, the required Fe concentration for the 18 nm Zn0.3Fe2.7O4@SiO2 nanoparticles is one tenth of that required for the 11 nm Fe3O4 nanoparticles.

Figure 1
figure 1

(a) ULF MRI system showing differential detector coil, B1(rf), (red) on either side of the shielded pre-polarization field, Bp, (purple) with applied magnetic field, B0, (blue). (b) ULF MRI gradient echo (GRE) sequence. Each pulse duration is marked in milliseconds (TR = 400 ms; TE = 27 ms). (c) Photograph of 16 mL vials used in ULF MRI imaging phantom.

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Figure 2
figure 2

ULF MRI 2D images of different SPION concentrations in 16 mL vials with a vial diameter of 14 mm: (a) 11 nm Fe3O4 solutions, (b) 16 nm Fe3O4 solutions, (c) 18 nm Fe3O4@SiO2 solutions, (d) 22 nm Fe3O4@SiO2 solutions, and (e) 18 nm Zn0.3Fe2.7O4@SiO2 solutions. The Fe concentrations of the solutions (in mM) are listed in the figures. DI water and MnCl2 (0.167 mM Mn in DI water) control samples are placed at the bottom of each image for normalization and comparison.

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Figure 3
figure 3

(a) The 0.13 mT MRI signals for different particle sizes versus Fe concentration are plotted in black dots (Fe3O4 11 nm), purple dots (Fe3O4 16 nm), red dots (Fe3O4@SiO2 18 nm), yellow dots (Fe3O4@SiO2 22 nm), and blue dots (Zn0.3Fe2.7O4@SiO2 18 nm) (b) Longitudinal relaxation rate (R1) versus Fe concentration of the solution in solid dots. (c) Transverse relaxation rate (R2) versus Fe concentration for the solution in solid dots. (d) Simulation of MRI signal versus Fe concentration with corresponding r1 and r2 relaxivity of each nanoparticles and TR = 400 ms, TE = 27 ms. (Lines included to help guide the eye.)

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Pulse sequence and relaxivities

T1 of the SPION solutions is measured with a prepolarization evolution pulse sequence34,35. In our setup B0 = 0.13 mT and T1 = 2.7 s for DI water and T1 = 0.12 s for the MnCl2 solution with Mn concentration of 0.167 mM. These results are comparable with SQUID based ULF MRI system of B0 = 0.128 mT, as reported in ref.35. R1 and R2 are linearly increasing as a function of the Fe concentration of five SPION solutions as shown in Fig. 3(b,c). The r1, r2, r2/r1 ratio, and ULF MRI maximum signal for the five SPION solutions are listed in Table 1. The important figures of merit for positive contrast are a large r1 value and a low r2/r1 ratio. This insures a large signal increase at low Fe concentrations. The 18 nm Zn0.3Fe2.7O4@SiO2 nanoparticles show a very high r1 = 615 s−1 mM−1, with only a modest increase in the r2/r1 = 2.7. In contrast, commercial high-field Gd-based T1 agents have r1 = 3 to 7 s−1 mM−1, with r2/r1 ~ 1.2 to 1.51.

Table 1 SPION relaxivities in s−1 mM−1 at 0.13 mT, where mM refers to the Fe concentration, and normalized MRI intensities.
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The MR signal is proportional to the transverse proton magnetization, Mt, at an echo time TE when the signal is acquired. Mt is a function of the pulse sequence parameters TR, TE and Fe concentration-dependent relaxation rates R1, R2 as described by the standard signal equation36

$$\begin{array}{c}{M}_{t}({C}_{Fe})={e}^{-TE\cdot {R}_{2}({C}_{Fe})}\cdot sin\alpha \cdot \frac{1+{e}^{-TR\cdot {R}_{1}({C}_{Fe})}-2{e}^{-(TR-\frac{TE}{2})\cdot {R}_{1}({C}_{Fe})}}{1+{e}^{-TR\cdot {R}_{1}({C}_{Fe})}\cdot cos\alpha }\end{array}$$
(1)

where CFe is Fe concentration, and α = π/2 is flip angle of rotation. We use Eq. 1 to simulate how the detected proton spin magnetization varies as a function of Fe concentration in the different SPION solutions, plotted in Fig. 3(d), and obtained good fits to our experimental data using the implemented pulse sequence parameters and measured relaxation rates. The highest value of r1 (615 s−1 mM−1) gives a 6 times enhanced MRI signal at low Fe concentrations (0.01 mM), which implies that ULF MRI may provide a technology for functional imaging using specially designed high-visibility SPIONs giving positive contrast.

The r1 and r2 values at high fields (3 T)

We measured the r1 and r2 values at high fields (3 T) using a standard inversion recovery sequence with variable inversion times for T1 and a spin echo sequence with variable echo time for T2. For the 16 nm Fe3O4 solutions we found that r1 = 11 s−1 mM−1 and r2 = 137 s−1 mM−1 (r2/r1 ratio of 12.5). After the high field MRI scan, the SPION solutions are sonicated and measured again with ULF MRI, and a reduction of the ULF MRI signal was observed, indicating that agglomeration of the SPIONs took place during the high-field MRI scan. Cluster or chaining of magnetic nanoparticles in large magnetic fields, due to their strong magnetic dipolar attraction, is a major limitation of high-field agents putting limits on the size of magnetic moments that can be utilized and creating stringent requirements on surface ligands to provide adequate separation. In comparison, repeat images in the ULF scanner showed no agglomeration effects, which is a significant advantage of ULF-MRI based nanoparticle contrast imaging.

Magnetic properties of nanoparticles and AC susceptibility

The room temperature magnetization versus applied magnetic field and zero field cooled/field cooled (ZFC/FC) loops of five SPION solutions are shown in Fig. 4(a,b). The closed Langevin-like hysteresis loops and low blocking temperatures (the temperature above which thermal energy overcomes anisotropy energy, causing the net moment of the particle to fluctuate randomly) indicate that all five types of nanoparticles are superparamagnetic at room temperature. The blocking temperatures of Fe3O4 nanoparticles are not linear with particle volume, which is possibly due to different magnetic anisotropy energy densities resulting from different synthetic conditions.

Figure 4
figure 4

Magnetic properties of magnetic nanoparticle solutions with concentrations of 1000 μg/mL, with Fe3O4 11 nm (black dots), Fe3O4 16 nm (purple dots), Fe3O4@SiO2 18 nm (red dots), Fe3O4@SiO2 22 nm (yellow dots) and Zn0.3Fe2.7O4@SiO2 18 nm (blue dots). (a) Magnetization versus applied magnetic field at room temperature. (b) Zero field cooled-field cooled curves with field strength of 20 mT, (c) Imaginary part of AC mass susceptibility (χ”) versus frequency response at 293 K. The dashed line indicates ULF MRI operating frequency of 5.56 kHz. (d) r1 vs. χ” at 5.56 kHz for the five nanoparticles sizes. (Lines included to help guide the eye).

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To better understand the T1 contrast enhancement mechanisms in SPION solutions at ultra-low field, we measured the imaginary part of the magnetic AC mass susceptibility (χ”) from 10 Hz to 250 kHz for five SPION solutions, shown in Fig. 4(c). The peak in χ” is attributed to either Brownian rotation of the nanoparticle or Néel relaxation of nanoparticle moment and occurs at a frequency that is given by the inverse of the nanoparticle moment relaxation time37,38,39. The magnetic fluctuation spectra are proportional to χ” through the fluctuation-dissipation theorem. We therefore expect strong proton spin T1 relaxation when proton resonant frequency (shown as the dashed vertical line in Fig. 4(c)) is near peaks in χ”, where nanoparticle magnetic fluctuation spectral density is large. We found that the χ” spectrum is flat for the 11 nm Fe3O4 solution compared to a higher frequency χ” peak observed at 198 kHz in the 16 nm Fe3O4 solution and at 100 kHz in the 18 nm Fe3O4@SiO2 solution. In comparison, a lower frequency χ” peak is observed at 1000 Hz in the 18 nm Fe3O4@SiO2 solution, at 250 Hz in the 22 nm Fe3O4@SiO2 solution and at 1000 Hz in the 18 nm Zn0.3Fe2.7O4@SiO2 solution. We calculated the Néel relaxation frequency of 18 nm Fe3O4@SiO2 with the measured magnetic properties and confirmed that the higher frequency of relaxation is Néel relaxation, and the lower frequency relaxation is Brownian relaxation as described in the Materials and Methods section.

We plot the measured r1 versus χ” at the proton resonance frequency of f0 = 5.56 kHz for the five different nanoparticles in Fig. 4(d). Also shown is a linear fit of r1 versus χ”(f0) showing a strong linear correlation. The large and tunable magnetic susceptibility of SPIONS cannot be obtained at high magnetic fields and is a unique attribute of ULF MRI.

Discussion

In SPION solutions, the longitudinal relaxation behavior is due to the relative motion of the water protons near the particle and the magnetic fluctuations of the nanoparticle through physical movement (Brownian translation and rotation) as well as intrinsic fluctuations of magnetic moment (Néel relaxation). According to the fluctuation dissipation theorem, the nanoparticle magnetic fluctuation spectral density should be proportional to the imaginary part of the magnetic susceptibility. These magnetic moment fluctuations give rise to fluctuating magnetic fields experienced by the water protons and lead to strong T1 relaxation of the proton spins. As seen in Fig. 4(c), it is possible to engineer the magnetic susceptibility and hence the magnetic fluctuations of the nanoparticles, over a wide range of frequencies. While the best sample studied here, the 18 nm Zn0.3Fe2.7O4@SiO2, had a peak close to the proton resonance frequency, if we adjust the particle properties or the resonant frequency we could get significant additional enhancement in T1 relaxivity and agent induced positive contrast. To obtain a high r1 value, we can tune either the magnetic properties of nanoparticle (moment and magnetic anisotropy energy) or mechanical properties (hydrodynamic shape and volume) to couple the χ” peak with the operating frequency of the ULF MRI. Although our highest r1 value is due to Brownian relaxation, which may be hindered in more biologically realistic viscous media, Néel relaxation (observed in 16 nm Fe3O4 nanoparticles) still gives appreciable contrast enhancement and can be tuned by engineering the magnetic anisotropy energy. Engineering Néel fluctuations can be done by changing either material properties, size, or shape of the particles, and is advantageous because this contrast will be independent of local tissue environment. Engineering the Brownian fluctuations has the advantage that the agents will give contrast only in special tissue environments (e.g. low viscosity environments) and the contrast may be turned on or off when binding or unbinding from a target.

ULF-MRI with high-visibility positive contrast agents provides a combination of good soft tissue contrast and functional imaging that is more deployable in a surgical suite or a doctor’s office. With new high-sensitivity optical magnetometers40 and advanced machine-learning based image reconstruction techniques41 coming online, radically new designs are possible with local field probes and coils. Viewing magnetic nanoagents as low frequency stochastic oscillators that strongly couple to nuclear spins, provides a path to greatly increase nanoparticle visibility. These systems may have unique applications for cell tracking, drug delivery monitoring, sentinel lymph node monitoring, and interventional procedures.

In summary, a 6-times T1 contrast enhancement for the 18 nm Zn0.3Fe2.7O4@SiO2 solution was achieved using room-temperature ULF MRI system. An extremely high value of r1 of 615 s−1 mM−1, over 100 times larger than commercial high field T1 agents, has been achieved. A linear relationship of r1 versus χ” at 5.56 kHz, the proton resonance frequency, was observed among all five different SPION solutions, which can be attributed to the magnetic fluctuations of the nanoparticles that relate to either Brownian motion or Néel relaxation. The ability to have large tunable magnetic susceptibility in SPIONS is a unique feature of ULF MRI and cannot be obtained in conventional high field MRI. The ULF MRI platform, combined with the use of designed SPIONs as high visibility positive contrast agents, therefore, creates new possibilities for safe inexpensive functional imaging.

Methods

Magnetic nanoparticle synthesis

The SPIONs have a magnetite structure (Fe3O4) as confirmed by X-ray diffraction (XRD) and transmission electron microscope (TEM)30. TEM images of the nanoparticles used in this study are shown in Fig. 5. In a typical synthesis of 11 nm Fe3O4 nanoparticles, a mixture of 5.0 mmol of iron acetylacetonate and 15.0 mmol of oleylamine, 3.0 mmol of oleic acid was heated at 200 °C under Ar atmosphere for 4 h. The black colored precipitate was subjected to magnetic separation and washed with a mixture of hexane and acetone several times to remove any uncoordinated amine and acid molecules. The 16 nm Fe3O4 nanoparticles were obtained with the increase of oleic acid concentration to 7.5 mmol. Finally, these amine-capped magnetic nanoparticles were dried at normal ambient conditions. To use these samples as MRI contrast agent, as-prepared Fe3O4 nanoparticles were subjected to surface modification with citric acid. 200 mg of the as-prepared Fe3O4 nanoparticles were dispersed in 20 mL of toluene and mixed with 20 mL of dimethylformamide (DMF) containing 20 mM of citric acid. Under Ar ambient, the mixture was then continuously stirred at 80 °C for 8 h. The final product was subjected to magnetic separation and was washed with ethanol several times to remove uncoordinated citric acid molecules. The SPIONs are diluted with deionized (DI) water and the particle concentrations ranges from 0.5 µg/mL to 200 µg/mL (Fe concentration from 0.0065 mM to 2.6 mM).

Figure 5
figure 5

TEM images of magnetic nanoparticles with 20 nm scale bar. (a) Fe3O4 nanoparticles with diameter of 11 nm, (b) Fe3O4 nanoparticles with diameter of 16 nm, (c) Fe3O4@SiO2 nanoparticles with 18 nm core diameter and 5 nm silica shell thickness, (d) Fe3O4@SiO2 nanoparticles with 22 nm core diameter and 5 nm silica shell thickness, (e) Zn0.3Fe2.7O4@SiO2 nanoparticles with 18 nm core diameter and 5 nm silica shell thickness. The ordering and agglomeration of the nanoparticles are due to the interactions when the suspended particles are dried on the TEM grids. The nanoparticles are dispersed during ULF-MRI relaxivity measurements.

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Nanoparticles with silica shells and core size of 18 nm Fe3O4@SiO2, 22 nm Fe3O4@SiO2, and 18 Zn0.3Fe2.7O4@SiO2 were synthesized by a one-pot solution method through thermal decomposition of a mixture of metal acetylacetonates with surfactants in a high-boiling point organic solvent31. Under a gentle flow of Ar, Iron(III) acetylacetonate (2.7 mmol), zinc(II) acetylacetonate (0.3 mmol), sodium oleate (2 mmol) and oleic acid (4 mL) were mixed with benzyl ether (20 mL). The mixture was magnetically stirred under a flow of Ar and then heated to 120 °C for 1 h. Under an Ar blanket, the solution was further heated to reflux (~300 °C) and kept at this temperature for 1 h. The mixture was then cooled down to room temperature by removing the heating mantle. The sizes of nanoparticles were tuned by controlling the heating rate during heating from 120 °C to 300 °C. The silica shells were coated on the hydrophobic nanoparticles via a reverse microemulsion method. The silica coating makes the nanoparticles hydrophilic, leading to aqueous dispersions stable for several years without agglomeration.

Néel/ Brownian relaxation modeling and connection between T1 and susceptibility

For application development, the Brownian and Néel relaxation characteristics of magnetic nanoparticles in solution need to be tailored by adjusting particle diameter, composition, and anisotropy (shape and/or crystalline). The dynamic response of a magnetic nanoparticle in solution is described by the complex magnetic susceptibility \(\,\overrightarrow{M}(\omega )=\overline{\overline{\chi }}\overrightarrow{{\rm{H}}}(\omega )\) where \(\overrightarrow{M}\) is the moment per unit volume and \(\overrightarrow{{\rm{H}}}\) is the magnetic field in A/m. At low frequencies, the susceptibility has a Debye form characterized by exponential relaxation times τB,N and corresponding relaxation frequencies \(2\pi {f}_{B,N}=\frac{1}{{\tau }_{B,N}}\), where the imaginary component of the susceptibility peaks. Néel relaxation dominates when the particle is fixed, and the magnetic moment rotates within the particle. Brownian relaxation dominates when the particle is free to rotate, and the magnetic moment is locked to the internal lattice. For in vivo biomedical applications, magnetic nanoparticles may be lodged in highly viscous tissues that reduce the Brownian rotation. The particle rotation needs to overcome the surface friction in a viscous fluid, which happens at a rotational frequency38,39

$$\begin{array}{c}{f}_{B}=\frac{{k}_{B}T}{8\cdot {\pi }^{2}\cdot \eta \cdot {{R}_{H}}^{3}}\end{array}$$
(2)

where, kB is Boltzmann’s constant, T is the temperature, η is the viscosity of the fluid and RH is the hydrodynamic radius of the nanoparticle. In the case of Néel relaxation the magnetic moment needs to overcome the anisotropy energy barrier and the fluctuation rate is given by

$$\begin{array}{c}{f}_{N}={f}_{0}\cdot exp(-\frac{{K}_{a}V}{{k}_{B}T})\end{array}$$
(3)

where Ka is the anisotropy energy density, V is the particle volume, and f0 is the attempt frequency, here chosen to be 1 GHz. The Ka of the particle is typically not that of the bulk material rather an effective Ka, influenced by the particle size, surface anisotropy, and magnetite core composition in combination, must be determined. These parameters are controlled using different synthesis processes. The effective anisotropy energy can be estimated from blocking temperature (TB) determined from the ZFC-FC measurements,

$$\begin{array}{c}{T}_{B}=\frac{{K}_{a}V}{{k}_{B}\cdot \,{ln}(\tau \cdot {f}_{0})}\end{array}$$
(4)

where τ is the measurement time.

The extracted Ka for 18 nm Fe3O4@SiO2 nanoparticle solutions, based on blocking temperature data (Fig. 4(b)) is Ka = 0.15 × 105 J/m3 and KaV/kBT ≈ 3.4 at zero field and room temperature, assuming small variation of Ka from the measurement temperature to room temperature. The calculated Néel relaxation frequency (Eq. 1) is fN = 134 kHz. The relaxation spectra (Fig. 4(c)) shows two peaks: one at 100 kHz and the other at 1 kHz corresponding to Néel and Brownian relaxation processes respectively. The Néel relaxation frequency of the 18 nm Fe3O4@SiO2 nanoparticle is too high to couple with proton Larmor frequency of current ULF MRI, but it could have potential imaging enhancement at low field MRI operating around 3 mT. Alternatively, one can increase Ka by doping29 or increase the particle volume to slow down the fluctuations.

There is an intrinsic connection between magnetic fluctuations and the imaginary part of the magnetic susceptibility given by the fluctuation-dissipation theorem42:

$$\begin{array}{c}{\mu }_{0}{\int }_{-{\rm{\infty }}}^{{\rm{\infty }}}\langle {M}_{\nu }(t){M}_{\mu }(t=0)\rangle {e}^{i\omega t}dt=\frac{\hslash }{V}coth(\frac{\hslash \omega }{2{k}_{B}T}){\chi }^{{\rm{^{\prime} }}{\rm{^{\prime} }}}\nu \mu (\omega )\end{array}$$
(5)

The magnetic fluctuations give rise to local field fluctuations that cause T1 relaxation, which in the simplest model43 is given by:

$$\begin{array}{c}\frac{1}{{T}_{1}}=4{\gamma }_{I}^{2}{b}^{2}\frac{{\tau }_{c}}{1+{\omega }^{2}{\tau }_{c}^{2}}\,\end{array}$$
(6)

where \(\,{{\boldsymbol{\gamma }}}_{{\boldsymbol{I}}}\) is the proton gyromagnetic ratio, b is the fluctuating magnetic field amplitude, \({{\boldsymbol{\tau }}}_{{\boldsymbol{c}}}\) is the relaxation time of the field fluctuations. To obtain large T1 relaxation, one needs the relaxation frequency to be close to the proton resonance frequency and have a large fluctuation field amplitude. Magnetic nanoparticles only have large fluctuations at low fields, where the Zeeman coupling between the particles’ moment and applied field is sufficiently small relative to thermal energy. At larger fields, Zeeman coupling dominates and the particles become saturated; that is, the net moment of each particle is locked in a unique orientation.

ULF MRI pulse sequences

The imaging MR pulse sequence is illustrated in Fig. 2(b); a pre-polarization field of 34.5 mT pre-aligns the water proton spins to provide a manageable MR signal that can be detected by the Faraday-coil. An AC magnetic field (B1), which drives protons at the Larmor frequency is applied for 1 ms to tip the spins away from B0 by 90 degrees. An 8 ms “grounding pulse” enables a relay that shorts the detector coil to ground to prevent ring-down noise from saturating the preamplifier. The repetition time (TR) is 400 ms, and the echo time (TE) is 27 ms.

For T1 measurements, a static field B0 = 0.13 mT is applied continuously. The prepolarizing field Bp = 20 mT is turned on for a period tp = 287 ms and switched off adiabatically, allowing the spins to relax for an evolution time tev in B0, before a standard spin-echo imaging sequence is applied. tev is varied between 0 s and 4 s, depending on the sample. The signal is proportional to the longitudinal magnetization after it has relaxed for a time tev. The observed signal versus tev is fit to a simple exponential decay model to obtain T1.

For T2 measurements, a static field B0 = 0.13 mT is applied continuously, and the prepolarizing field Bp = 20 mT is turned on for a period tp = 287 ms. The evolution time tev = 22 ms is now fixed, after which a 90-degree tipping pulse is applied, followed at a time TE/2 by a 180-degree refocusing pulse. The free induction decay is acquired at a time TE and is proportional to the transverse magnetization after it has decayed for a time TE. TE is varied, and the observed signal versus TE is fit to a simple exponential decay model to obtain T2.

The relaxivities are then calculated by plotting R1 = 1/T1, R2 = 1/T2 vs Fe concentration, using the slope of a linear fit to the data.

Magnetic properties measurement

Magnetization versus applied magnetic field (M-H) loops and zero field cooled-field cooled (ZFC-FC) loops are measured using a SQUID magnetometer, as shown in Fig. 3(a,b). The SPION solutions were heat-sealed in polypropylene containers with a particle concentration of 1.0 mg/mL and a mass of about 160 mg. The diamagnetic components are subtracted from the M-H loops using the known mass of the water and sample container. The ZFC-FC loops are measured using the same SPION samples under presence of a 20 mT magnetic field after the initial zero field cooling phase. As shown in Fig. 4(b), the room temperature imaginary part of AC mass susceptibilities of the SPION solutions were measured with a commercial AC susceptometer using SPION solutions with a particle concentration of 1.0 mg/mL, a mass of approximately 180 mg, and an applied AC field of 398 A/m. The ZFC-FC and the AC-susceptibility measurements are done in low magnetic fields, so we expect that the nanoparticles will remain dispersed and in a similar state as probed in the ULF-MRI. When high field measurements are performed, as seen in Fig. 4a, agglomeration and chaining of the nanoparticles may take place altering the magnetic properties.

Data and materials availability

All data needed to evaluate the conclusions in the paper are present in the paper. Additional data related to this paper may be requested from the authors.