Abstract Body:

Magnetic Particle Imaging (MPI) is an emerging positive-contrast imaging modality that directly images superparamagnetic iron oxide (SPIO) tracers in the body with excellent contrast, sensitivity and zero radiation [1]. To optimize MPI resolution and sensitivity, we must  understand the SPIO Brownian and Néel relaxation times, which are as important in MPI as T1 and T2 relaxation times are in MRI.   Over the last 5 decades,  nanoscale physicists have theorized how relaxation times depend on particle size, shell thickness, medium viscosity, and the applied field strength [2–5]. Here, we use a novel method of pulsed magnetic field relaxometry to measure relaxation times over a range of magnetic field amplitudes and viscosities, providing the first experimental validation of relaxation theories. The alignment of an SPIO to an external field can be either a Brownian process (where the entire nanoparticle and shell physically rotate together) or a Néel process (where only the electronic domain aligns).  The relaxation mechanisms work in parallel, so the faster mechanism dominates [4, 6]. Note that the instantaneous Neel relaxation time varies by 3 orders of magnitude during each  MPI scan, due to the field dependence of relaxation. 

Objective: Here we aim to show that: (a) experimental relaxation times match the variation with magnetic field strength predicted by theory [2-5]; and that (b) experimental Brownian relaxation times vary linearly with viscosity.  Square wave relaxometry was performed on commercial SPIO nanoparticles to determine their relaxation time constants as a function of magnetic field strength, magnetic core size, and viscosities [7, 8]. Theoretical relaxation times for the particles were calculated using numerical linear algebra techniques on the Fokker-Planck equations governing Brownian and Néel relaxation, and these were compared to experimental data [8]. Transmission electron microscopy (TEM) and dynamic light scattering (DLS) were used to determine ab initio physical parameters for the theoretical models.  

Methods: Single-core and clustered magnetite nanoparticles with magnetic core diameters ranging between 5 and 30 nm were purchased from commercial vendors in both organic and aqueous solvent dispersions. Pulsed relaxometry was performed using the Berkeley Arbitrary Wave Relaxometer/Spectrometer (AWR) [7] with a range of viscosities. Square wave current waveforms were used to generate alternatingly polarized, pulsed solenoidal magnetic fields with amplitudes between 1 mT and 12 mT. Pulses had a period of 1 ms with 50% duty cycle and a 4 μs rise time. The waveform was averaged across periods to obtain an exponential decay function with time constant agnostic to particle concentration and magnetization.

Results: The experimentally measured relaxation spectrum showed excellent agreement with theory obtained from the literature and from numerical solutions to the Fokker-Planck equations. The relaxation times were also observed to be a strong function of magnetic core diameter and viscosity and core diameters between 15 nm and 30 nm showed excellent agreement with ab initio theory, as shown in Figs. [A-D].

 Conclusion: We have successfully measured the MPI relaxation times as a function of core size, applied magnetic field and viscosity and provided the first experimental confirmation of both theoretical models and Fokker-Planck simulations [2-5].  We have also demonstrated that Brownian relaxation varies linearly with viscosity, as predicted by theory [4].  This is exciting for molecular imaging, because Brownian relaxation could provide the first direct imaging method to distinguish bound from unbound magnetic nanoparticles. Magnetic field-based pulsed relaxometry could soon allow for measuring intracellular viscosity at depths unattainable by optical methods with only minor modifications to MPI tracers, hardware, and pulse sequences. 

Image/Figure:

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Image/Figure Caption:

Figure 1. (A) Comparison between experimental data and theory shows good agreement across multiple nanoparticle samples including suspensions of Imagion PrecisionMRX particles in (A1) organic solvent (A2) and water and (A3) Micromod synomag-D clusters in water; (B) Experimental characterization of relaxation times as a function of nanoparticle magnetic core diameter agrees with theoretical predictions. Particles smaller than 15 nm relaxed faster than the pulsed relaxometry limit of detection and are not shown; (C) Pulsed magnetic field viscometry using Brownian nanoparticles shows strong positive linear correlation between the measured relaxation time constant and viscosity. Viscous samples of glycerol-nanoparticle mixtures show the expected linear trend at both 2 mT and 12 mT excitation amplitudes. (D) Pulsed relaxometry using temperature to continuously vary viscosity in the 2 cP to 6 cP range showed a highly linear dependence of the Brownian relaxation time constant on viscosity. 

Author

Chinmoy Saayujya
University of California, Berkeley