Phase-Encoded Hyperpolarized Nanodiamond for Magnetic Resonance Imaging

Surface-functionalized nanomaterials are of interest as theranostic agents that detect disease and track biological processes using hyperpolarized magnetic resonance imaging (MRI). Candidate materials are sparse however, requiring spinful nuclei with long spin-lattice relaxation (T1) and spin-dephasing times (T2), together with a reservoir of electrons to impart hyperpolarization. Here, we demonstrate the versatility of the nanodiamond material system for hyperpolarized 13C MRI, making use of its intrinsic paramagnetic defect centers, hours-long nuclear T1 times, and T2 times suitable for spatially resolving millimeter-scale structures. Combining these properties, we enable a new imaging modality, unique to nanoparticles, that exploits the phase-contrast between spins encoded with a hyperpolarization that is aligned, or anti-aligned with the external magnetic field. The use of phase-encoded hyperpolarization allows nanodiamonds to be tagged and distinguished in an MRI based on their spin-orientation alone, and could permit the action of specific bio-functionalized complexes to be directly compared and imaged.

For conventional MRI sequences, the fundamental MRI resolution limit is reached when the NMR linewidth is approximately equal to the frequency separation between each pixel [5]: Where dz is the pixel length, γ the nuclear gyromagnetic ratio, G is the peak gradient strength, and T * 2 is the transverse coherence time. Our nanodiamond samples have T * 2 ∼ 1 ms, which corresponds to a resolution limit of 0.4 mm in our microimager (250 mT/m peak gradient strength). Increasing the resolution beyond this point will require the use of more complex MRI sequences incorporating such features as multipulse line narrowing [6].

Supplementary Note 3: 13 C Enrichment
Isotopic enrichment of the concentration n of spin-1/2 nuclei in nanoparticles is attractive for the proportional increase in MRI signal. Whilst increased MRI signal alone is valuable, if electron lifetimes are sufficiently short, the increase of the spin diffusion rate [7,8] in enriched samples may also reduce the duration of DNP required to reach high nuclear polarizations. These improved properties may be achieved whilst maintaining long nuclear T 1 times, with studies of 99% 13 C enriched bulk diamond having shown spin-lattice relaxation times of several hours. However, in enriched samples, the dipolar coupling strength between spins increases due to decreased interspin spacing, giving an NMR linewidth δ 1/2 that is proportional to n. Thus, increasing n carries an inversely proportional reduction in T * 2 and corresponding reductions in imaging sensitivity. In light of these considerations, we believe isotopic enrichment of spin-1/2 nuclei up to 10% abundance will reveal the ideal compromise between high magnetizations and long spin-spin relaxation times.

Supplementary Note 4: Stability of nanodiamond solutions
Dynamic light scattering (DLS) measurements showed that the 2 µm HPHT diamonds used in this work have a zeta potential of -38±7 mV in water. The 210 nm HPHT NDs have a near identical zeta potential of -39 ± 8 mV. DLS measurements of particle size and zeta potential were performed in a Zetasizer Nano ZS. Nanoparticle dispersions were prepared by sonication. DLS size measurements agreed with specifications provided by the manufacturer. Such a large, negative zeta potential means that these HPHT diamonds are highly aggregation-resistant in aqueous solution, making them well suited to injection and biological applications that require surface functionalization [9]. The 2 µm particles display sedimentation from aqueous solution on the timescale of hours, whilst little sedimentation was observed in solutions of 210 nm HPHT NDs over a period of weeks. This difference in sedimentation phenomena occurs due to the relative size of gravitational forces and Brownian motion as we show through a calculation of the Péclet number P e . The Péclet number is a dimensionless measure of the relative effects of flow and thermal diffusion [10] and, for a particle in suspension, is given by: Where m R is the buoyant mass of the particle (mass of particle minus mass of displaced solvent), g is acceleration due to gravity, a is the particle radius, k B is the Boltzmann constant and T is the temperature. For P e 1, gravity dominates over Brownian forces, leading to sedimentation in the absence of other hydrodynamic forces.
We can calculate a P e of 0.003 for our 210 nm particles if we assume spherical particles, diamond density of 3510 kg m −3 and water density of 1000 kg/m 3 . Similarly, we can calculate a P e of 25 for the larger 2 µm diamond particles. Of interest is the critical diamond size of 504 nm where P e = 1, such that Brownian forces and gravitational forces are balanced.
These values explain the sedimentation of the 2 µm diamond particles.

Supplementary Note 5: Conditions for adiabatic transfer
Moving hyperpolarized samples through changing magnetic fields during sample transfer from the polarizer to MRI system results in fluctuation of the Zeeman energy between spinup and spin-down states. If the rate of change of the magnetic field is comparable to the Larmor frequency the polarization state may change. To ensure this does not occur, the adiabatic parameter A must be much less than one at all times during the transfer process.
We can calculate the adiabatic parameter from [11]: Where γ n is the nuclear gyromagnetic ratio, B is the magnetic field and d B dt the rate of change of the magnetic field. When d B dt and B are parallel, as is the case when the sample enters and exits a superconducting magnet, the cross-product in Eq. 1 is zero and adiabaticity is maintained. This means that transfer is adiabatic when the sample exits the hyperpolarizer and enters the MRI system. However, we must also consider the situation where the sample enters the 380 mT Halbach array used for sample transfer, as the magnetic field in this array is perpendicular to B 0 of the superconducting NMR magnets. From an analysis of our transfer process, we estimate a minimum B = 5 mT perpendicular to a For a 13 C nucleus, these values give A = 0.09, confirming the adiabatic nature of our transfer process.  [12,13]. The hyperfine-split component is attributed to P1 centers (linewidth 0.1 mT), substitutional nitrogen atoms in the diamond lattice [14].