Introduction

Superparamagnetic iron oxide nanoparticles (IONP) are versatile MRI contrast agents for applications in cell tracking, blood volume measurement or assessment of barrier function. Relaxation time mapping enables quantification of local effects of IONPs on MR relaxation. However, concentration or spatial distribution of IONPs cannot be directly derived from such measurements since relaxation times depend on their exact physico-chemical properties¹. Here, we implemented a simulation pipeline to characterize the relation between relaxation times and physico-chemical properties for two IONPs.

Methods

Monte Carlo simulations were implemented to predict the change of transverse relaxation times T₂/T₂^* in the presence of IONP-based contrast agents with distinct physico-chemical properties^2,3 (Fig. 1). Inside a cubic voxel (0.000001–0.001 mm³) IONPs were modeled as randomly distributed impermeable spheres, giving rise to local dipole fields. Diffusion of 5,000 to 10,000 water molecules was modeled as random walk for 100 ms. The phase of each spin was accrued over a given number of diffusion steps (100,000–10,000,000) through the local dipole fields. The MR signal at each diffusion step was obtained by summing over all simulated spins and T₂^* was calculated with an exponential fit of the signal. For T₂ simulations, a multi-spin-echo-sequence (echo spacing: 6.5 ms, 15 echoes) was implemented and phases of all spins were inverted after each refocusing pulse.
Simulations were parameterized to reproduce two nanohybrid particles, which both comprised an identical superparamagnetic magnetite core of ~16 nm diameter with a saturation magnetization of 62 Am²/kg. The two IONPs differed in preparation strategies, one is based on encapsulation of the IONP with an amphiphilic comb polymer poly(maleic anhydride alt-1-octadecene) (PMAO) and the other involves a ligand-exchange procedure at the IONP using tetramethyl ammonium hydroxide (TMAOH). The hydrodynamic radii of both particles were lognormally distributed, as measured by dynamic light scattering (DLS) (Fig. 2). Average radii of PMAO- and TMAOH-particles were 76 nm and 130 nm, respectively.
For MRI, the particles were prepared in agarose phantoms in iron concentrations of 90, 180 and 400 µmol/L. Measurements were performed on a 9.4 T animal scanner (Bruker BioSpec 94/20). For T₂ measurements, a spin-echo-sequence with variable echo times (T_{E, min}: 6.5 ms, echo spacing: 6.5 ms, 16 echoes, T_R: 2000 ms) and for T₂^* measurements ultra-short-echo-sequences (T_{E, min}: 0.45 ms, T_{E, max}: 40 ms, T_R: 120 ms, flip angle: 20°) were used.
Simulation of the MR measurements was performed for concentrations of 90, 180 and 400 µmol/L Fe, for constant radii of 76 nm and 130 nm, and for lognormally distributed hydrodynamic radii. To account for potential particle aggregation, simulations were performed with different hydrodynamic radii from 30 to 500 nm. Each simulation took between 30 s to 140 min on a high-performance-computing cluster and was repeated three times.

Results

MRI measurements showed linearly increasing transverse relaxation rates R₂/R₂^*, with higher concentration for both IONPs (Fig. 2, 3). Relaxivities were r₂ = 422.3 $$$\pm$$$ 4.3 Lmmol^-1s^-1, r₂^* = 634 $$$\pm$$$ 16 Lmmol^-1s^-1 for PMAO-particles and r₂ = 74 $$$\pm$$$ 19 Lmmol^-1s^-1, r₂^* = 862.0 $$$\pm$$$ 9.8 Lmmol^-1s^-1 for TMAOH-particles. Relatively large differences between R₂ and R₂^* were observed for TMAOH-particles.
Simulations of the MR experiments reproduced the linear correlation between the concentration and R₂/R₂^* for both IONPs (Fig. 3). Simulations with constant radii reproduced R₂/R₂^* values for the PMAO-particles well but differed substantially for higher concentrations of the TMAOH-particles. Using distributed hydrodynamic radii, had minor effects on R₂, but increased R₂^*, which for the TMAOH-particles perfectly matched the measured data.
Simulations of different hydrodynamic radii showed, that R₂^* was largely independent of the radius, whereas R₂ decreased with increasing radius (Fig. 4). While the simulation reproduced measured R₂^* for both particles, measured R₂ values for the TMAOH-particles were lower, suggesting larger particle radii (distributed around 300 nm) than observed with DLS. High resolution MRI of a TMAOH phantom sample indeed suggested substantial particle aggregation (Fig. 5).

Discussion

The implemented simulations were able to reproduce experimentally measured R₂/R₂^*. Relaxation rates increased for higher IONP concentrations and for larger radii (TMAOH, but not PMAO) a pronounced difference between R₂ and R₂^* was reproduced.
Using lognormally distributed radii hardly affected R₂ values. However, for R₂^*, larger values were obtained that matched the experimental data for the TMAOH-particles. The remaining differences in R₂ for the TMAOH-particles can be explained by particle aggregation with radii distributed around 300 nm (Fig. 4, 5).
Both, measured and simulated differences in R₂ and R₂^* for the IONPs agree with relaxation theory^4,5. Small IONPs are described by the motional averaging regime (MAR), where R₂ and R₂^* are comparable and increase with increasing radius. Larger IONPs fall in the static dephasing regime (SDR), where R₂^* is independent of the radius, and the echo-limited regime (ELR), where R₂ decreases with increasing radius. PMAO-particle radii are between the MAR and SDR, while TMAOH-particle radii fall in the SDR and ELR.

Conclusion

Our simulations are suitable to quantify the influence of IONP-based contrast agents on transverse relaxation times. Here, the combination of measurements and simulations was able to unveil particle aggregation from known concentrations. In future cell tracking studies with known intracellular iron distribution, our simulations may enable exact quantification of infiltrated cells in a given tissue region.

Acknowledgements

No acknowledgement found.