Magnetic resonance imaging (MRI) phantoms are routinely used for calibrating MRI machines and characterizing the MRI system performance, such as resonance frequency, spin–spin and spin–lattice relaxation times, signal-to-noise ratio, image uniformity, spatial resolution, and phase related image artifacts [1]. Phantoms should be non-toxic, stable, inexpensive, easy to use and desirably having relaxation times comparable to those of human tissues. Two types of MRI phantoms are commonly used: aqueous solutions and gels. The aqueous solutions of paramagnetic salts such as CuSO4, NiCl2, MnCl2, or GdCl3 exhibit homogeneous spin–lattice (T1) and spin–spin (T2) relaxation times throughout the phantom and long-term stability. Herewith, the liquid phantom needs some stabilization time before the measurement. Gel phantoms include agarose, agar, polyvinyl alcohol, gelatin, gelatin-agar, or some other medium with the addition of paramagnetic substances (usually GdCl3) to adjust the relaxation time [2]. However, the aforementioned compounds are toxic [3,4,5,6], and their handling, shipping and disposal are questionable owing to possible contamination of the MRI equipment and personnel. Therefore, the scientific community continues to develop new phantoms that would be free of the aforementioned disadvantages and would validate the accuracy of the in vivo measurements, as well as repeatability and reproducibility of measurements across imaging platforms and time.

To this end, Sękowska et al. have recently reported on the eventual application of detonation diamond nanoparticles in phantoms for MRI [7]. The phantoms were produced using distilled water, agar (1.413%) and carrageenan (2%) with addition of the detonation nanodiamond (DND) particles of the average size of 4–5 nm suspended in dimethyl sulfoxide (DMSO) and treated by 5-min-long high-power ultrasound sonication. The content of the DND-DMSO suspension in prepared phantoms was set to 0%, 8%, 10% and 12%, respectively. The contents were thoroughly mixed, poured into molds and placed to congeal. Surprisingly, the authors obtained a linear dependence of the spin–lattice (T1) and spin–spin (T2) relaxation times of the phantoms on the nanodiamond concentration (See Figures 3 and 5 in ref [7].). This result contradicts our recent experimental nuclear magnetic resonance (NMR) data on DND suspensions [8,9,10], as well as some fundamentals of the relaxation phenomena in nuclear spin systems [11, 12].

Let us now analyze the nuclear relaxation data in our DND suspensions and discuss whether these compounds can be used as MRI phantoms. As it is well known, DND particles exhibit intrinsic localized paramagnetic defects: (i) P1 nitrogen paramagnetic defects distributed throughout the diamond core and (ii) unpaired electron spins of dangling bonds positioned mainly in the near-surface layer [13,14,15]. The overall defect density in the DND particles measured by EPR is around 6 × 1019 spin/g [13,14,15]. In DND suspensions, the relaxation of the proton nuclear spins of the solvent is accelerated owing to the interaction of protons with unpaired electron spins of the aforementioned paramagnetic defects [8,9,10]. The contributions of the DND-inherent paramagnetic defects to the experimentally measured proton spin–lattice and spin–spin relaxation rates \(R_{1}^{\exp }\) and \(R_{2}^{\exp }\) in suspensions are described by the second term of equations [8]

$$R_{1}^{\exp } = \frac{1}{{T_{1}^{\exp } }} = \frac{1}{{T_{1}^{{{\text{solv}}}} }} + \frac{1}{{T_{1}^{{{\text{DND}}}} }} = R_{1}^{{{\text{solv}}}} + r_{1}^{{{\text{DND}}}} \times C_{{{\text{DND}}}}$$
(1)
$$R_{2}^{\exp } = \frac{1}{{T_{2}^{\exp } }} = \frac{1}{{T_{2}^{{{\text{solv}}}} }} + \frac{1}{{T_{2}^{{{\text{DND}}}} }} = R_{2}^{{{\text{solv}}}} + r_{2}^{{{\text{DND}}}} \times C_{{{\text{DND}}}}$$
(2)

where \(T_{1}^{{{\text{solv}}}}\) and \(T_{2}^{{{\text{solv}}}}\) are the spin–lattice and spin–spin relaxation times of the solvent, \(T_{1}^{{{\text{DND}}}}\) and \(T_{2}^{{{\text{DND}}}}\) are the spin–lattice and spin–spin relaxation times caused by paramagnetic defects of the nanodiamond particles, CDND is the concentration of DND particles in suspensions, and r1 and r2 are the relaxivities defined as the slopes of the concentration dependences of \(\frac{1}{{T_{1}^{\exp } }}\) and \(\frac{1}{{T_{2}^{\exp } }}\). Here \(T_{1}^{{{\text{solv}}}}\) and \(T_{2}^{{{\text{solv}}}}\) are the characteristics of the specific liquid solvent used and, therefore, are constant for all measurements.

The results of our measurements of the spin–lattice and spin–spin relaxation times and rates of water protons in aqueous DND suspensions as a function of the DND concentration are shown in Figs. 1 and 2. The data show that the paramagnetic defects of the DND particles (i) affect the relaxation rates of protons in suspension and (ii) reveal linear dependence of the relaxation rates \(R_{1}^{{{\text{DND}}}}\) and \(R_{2}^{{{\text{DND}}}}\)(not relaxation times!) on the DND content, which is fully consistent with the fundamentals of the spin relaxation theory [11, 12], revealing a linear proportionality of the relaxation rate to the concentration of paramagnetic defects. This is a universal law, which is valid for liquids, gels, and solids (for example, see Reviews [14,15,16]). Herewith, as it follows from Eqs. 1 and 2 and the experimental data shown in Figs. 1 and 2, both proton spin–lattice and spin–spin relaxation times exhibit a hyperbolic dependence on the nanodiamond concentration CDND in suspension:

$$T_{1} = \frac{1}{{R_{1}^{{{\text{solv}}}} + r_{1}^{{{\text{DND}}}} \times C_{{{\text{DND}}}} }}$$
(3)
$$T_{2} = \frac{1}{{R_{2}^{{{\text{solv}}}} + r_{2}^{{{\text{DND}}}} \times C_{{{\text{DND}}}} }}$$
(4)
Fig. 1
figure 1

Dependence of the spin–lattice relaxation rate R1 and spin–lattice relaxation time T1 of water protons in aqueous DND suspensions on the concentration of DND particles in suspensions

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Fig. 2
figure 2

Dependence of spin–spin relaxation rate R2 and spin–spin relaxation time T2 of water protons in aqueous DND suspensions on the concentration of DND particles in suspensions

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These experimental results are in complete agreement with the published literature and the fundamentals of relaxation phenomena in nuclear spin systems. We note that similar hyperbolic-like concentration dependence of T1 was recently obtained in measurements of the 1H spin–lattice relaxation of aqueous solutions of nanodiamonds of 18 and 125 nm in diameter, prepared by the high pressure–high temperature (HPT) technique [17]. These results support well my above findings.

Recently, Thangavel et al. [18] measured the relaxivities r1 and r2 in aqueous solutions of common paramagnetic agents (CuSO4, MnCl2, and NiCl2) at room temperature and a magnetic field of 3 T. Separate phantoms were prepared at various concentrations from 0.05 to 0.5 mM for MnCl2 and from 1 to 6 mM for CuSO4 and NiCl2, and were reported to reveal relaxivities r1 = 0.602 mM−1 s−1 and r2 = 0.730 mM−1 s−1 for CuSO4, r1 = 6.397 mM−1 s−1 and r2 = 108.266 mM−1 s−1 for MnCl2, r1 = 0.620 mM−1 s−1 and r2 = 0.848 mM−1 s−1 for NiCl2 (Table 1). Our nanodiamond suspensions showed relaxivities r1 = 2.1 mM−1 s−1 and r2 = 15.8 mM−1 s−1 in B0 = 8 T [8], which are higher than those of CuSO4 and NiCl2 and lower than that of MnCl2. We note that our measurements were done in in B0 = 8 T, and since r1 and r2 increase with decreasing magnetic field [19], we expect that the DND suspensions will show several times higher relaxivities in magnetic fields from 1 to 3 T used in clinical MRI scanners.

Table 1 Relaxivities r1 and r2 of several MRI phantoms
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In conclusion, we also note that the amount of paramagnetic defects in DND can be increased by irradiation [20], which would lead to higher relaxivities. Herewith the relaxation time T1 = 805 ms for a DND concentration of 4.64 mM in our suspension coincides with the relaxation time of the human tissue T1 = 810.5 ms [7]. It is important that the DND suspensions are non-toxic, very stable and do not undergo noticeable changes and precipitation during several years of storage. They are robustly processed, safe, readily available, inexpensive and easy to handle. Therefore, summarizing all of the above, nanodiamonds can be considered suitable for use as MRI phantoms.