Introduction

Magnetic nanoparticles (MNPs) have emerged as versatile and highly effective contrast agents in nuclear magnetic resonance imaging (MRI) and have played a pivotal role in advancing this crucial medical imaging tool. Globally, over one hundred million MRI procedures are conducted annually, one-third of which employ magnetic contrast agents to enhance imaging precision and sensitivity [1]. The synthesis, functionalization, and evaluation of MNPs as MRI contrast agents have attracted considerable attention [2, 3]. As researchers have investigated the properties of MNPs, their structural control has played a crucial role in their ongoing evolution and refinement to improve their MRI contrast power. In T₁-weighted MRI, under the magnetic field strength range of medical and research scanners, the inorganic structure of MNP contrast agents has a larger influence on their r₂ values (transverse relaxivity) than their r₁ values (longitudinal relaxivity) [4]. Moreover, reducing the structure-sensitive r₂ value can suppress T₂ effects (negative contrast) and increase the essential r₁/r₂ ratio, which will enhance the T₁ effect (positive contrast) of the MNPs [5]. In this regard, both computational and experimental methods have been developed for structural control to optimize MNPs and unlock their full capabilities. Computational methods, such as modeling simulations, have the advantage of easily changing the MNP structures, including varying the MNP lattice or size parameters, to predict their T₁ or T₂ contrast power. After changing the synthesis conditions to produce MNPs of the desired size, an effective structural analysis tool is necessary to confirm that the as-synthesized MNPs have the targeted structures needed to obtain the ideal contrast power. In this regard, high-sensitivity and high-resolution X-ray absorption fine structure (XAFS) spectroscopy can identify both the electronic and geometric structures of materials [6,7], revealing the local atomic environment to shed light on the bond lengths and angles, coordination numbers, and local symmetry [8, 9]. Therefore, it is crucial to combine modeling simulations and XAFS spectroscopy to achieve structural control of MNPs and achieve the best MRI performance.

From a computational perspective, analytical and simulation models have been established to predict the optimal structure of MNPs processing an ideal MRI contrast power depending on their specific applications [10-13]. Using these models, only the production and evaluation of a narrower set of MNPs are required to save a large amount of energy and materials. To obtain statistically reliable results, the time-domain step size of the simulation is set to be proportional to the square of the MNP diameter (Eq. 1 and Eq. 5); in other words, the corresponding simulation time (the reciprocal of the step size) for small MNPs is much higher than that for large MNPs (e.g., 1-nm MNPs take 10² times longer than 10-nm MNPs). Consequently, it is difficult for traditional algorithms and computing resources to simulate MNPs smaller than 5 nm because of their formidable simulation time, which can be on the scale of months. In biomedical applications, small MNPs are particularly important, with a size of <5.5 nm being a critical criterion [14, 15] because MNPs smaller than this can be rapidly cleared through the kidney route in humans and mammals after intravenous injections, diminishing potential post-imaging side effects. Hence, there is a pressing need for a faster simulation method to accurately predict the r₁ or r₂ values of MNPs smaller than 5 nm. After simulation and synthesis, verifying the structure of these super-small MNPs poses another challenge to characterization tools [16]. Fortunately, the XAFS technique, using an intense and tunable synchrotron radiation X-ray source, is ideal for determining the structures of metallic compounds at a high-resolution Angstrom (Å) scale [17-19]. So far, the XAFS technique has been used to investigate superparamagnetic iron oxide nanoparticles (SPIONs) with a size of >8 nm [20, 21] because their stable magnetization and potentially minimized toxicity make SPIONs the ideal type of MNPs for biomedical MRI applications [22]. However, it has traditionally been challenging to synthesize monodisperse SPIONs smaller than 8 nm while satisfactorily maintaining their crystal structure and superparamagnetism [23]. Therefore, the availability of these smaller SPIONs has limited their use in MRI applications in the past. More recently, small SPIONs have become increasingly popular due to their excellent T₁ contrast power [24, 25], whose bright signals are preferred by MRI radiologists over the dark signals of T₂ contrast from large SPIONs. Nevertheless, the magnetic and structural properties of these newly synthesized small SPIONs are less characterized, and the structural knowledge of < 8 nm SPIONs revealed by the XAFS technique is lacking. Because the XAFS technique is a powerful tool for accurately determining the local atomic and electronic structures of various materials, a comprehensive investigation of SPIONs smaller than 8 nm using XAFS is highly needed.

Herein, we report a novel two-pronged computational and experimental strategy that combines MATLAB-based simulations and XAFS analysis to develop small SPIONs best suited for MRI. Our MATLAB-based simulation method is empowered by a swift matrix operation algorithm [26] and parallel computing ability [27] to achieve high-speed prediction of the MRI contrast power for SPIONs smaller than 8 nm. We simulated 1-, 2-, 3-, 6-, and 8-nm SPIONs and obtained statistically reliable results within one week, showing that SPIONs with inorganic diameters between 1 and 3 nm outperformed their larger counterparts. To experimentally validate our predictions, we synthesized small SPIONs, followed by the characterization and evaluation of their magnetic properties, MRI contrast powers (r₁ and r₂ values), and MR imaging performances in vivo in mice. Furthermore, we demonstrated that XAFS using a synchrotron radiation X-ray source could successfully reveal the atomic and electronic structures of these small SPIONs, thereby explaining their magnetic origins. Overall, the as-synthesized SPIONs exhibited attractive structural, magnetic, and imaging characteristics for use in biomedical MRI applications. On the one hand, the computational results could guide and facilitate MNP synthesis through simulation; on the other hand, the experimental XAFS measurements could reveal the MNP structures and underlying mechanisms of their outstanding properties. Thus, our two-pronged computational and experimental strategy provides a convenient and rigorous platform for developing future MRI probes.

MRI simulation theory

Computational MRI studies include analytical and simulation models. Analytical models [10, 11, 28] are derived from theoretical MRI equations by applying reasonable approximations (e.g., strong magnetic field, long blood vessel, and low iron concentration approximations) under specific circumstances. These analytical models can directly calculate the r₁ or r₂ values of MNPs without any simulation; thus, the calculation processes are fast. However, the r₁ or r₂ results provided by analytical models are usually a single number without accurate statistical information, such as the standard deviation calculated from numerical simulations. Moreover, some of the above approximations cannot be applied to all types of MNPs in general. In particular, newly structured MNPs will have even higher discrepancies than conventional MNPs. Consequently, simulative models that follow the MRI theory without any major approximation were established. Simulation models [12, 13, 29, 30] utilize modern computers to accurately calculate the r₁ or r₂ value of MNPs, which often yield statistically reliable results. The established principles of these MNP simulation models [31, 32] are described below.

In biological media, the movement of water molecules follows the pattern of Brownian motions, where they randomly walk in a three-dimensional (3-D) space and generate proton trajectories. The step size of this 3-D random walk of water molecules, $\sigma$, is found as follows: $\sigma =\sqrt{6D\text{Δ}t},$ (1) where $D$ is the diffusion constant of water (2.5 × 10^-9 m²/s), and Δt is the step size in time. To ensure that $\sigma$ has the same order of magnitude as the MNP diameter ($2r_{\text{NP}}^{}$, where $r_{\text{NP}}^{}$ is the MNP radius) for meaningful MRI simulations, Δt must have the same order of magnitude as $\frac{2r_{\text{NP}}^2}{3D}$. The protons of these water molecules experience magnetic field perturbations induced by the MNPs, and their projection along the z-axis ($B_z$ component) given by spherical MNPs is as follows [33]: ${\left(B_z\right)}_{i,k}=\sqrt{\frac{5}{4}}\cdot \frac{r_{\text{NP}}^3\text{Δ}{\omega }_r}{\gamma \cdot d_{i,k}^3}\cdot \left(3{\text{cos}}^2{\theta }_{i,k}-1\right),$ (2) where the z-axis is the major axis along the main static magnetic field ($B_0$) of the MRI scanner, i denotes the i^th step of the random walk of a proton, k denotes the k^th MNP, $r_{\text{NP}}^{}$ is the MNP radius, $\text{Δ}{\text{ω}}_{\text{r}}$ is the root-mean-squared angular frequency shift at the MNP surface/equator (2.36 × 10⁷ rad/s for magnetite and 1.95 × 10⁷ rad/s for maghemite), $\gamma$ is the gyromagnetic ratio of the proton (2.68 × 10⁸ rad s^-1 T^-1), $d_{i,k}^{}$ is the 3-D distance between the i^th position of the proton and the center of the k^th MNP, and ${\theta }_{i,k}$ is the tilt angle between the z-axis and direction vector from the k^th MNP to the i^th position of the proton. Because the total magnetic field perturbation is the linear sum of the MNP perturbations, ${\left(B_z\right)}_{i,k}$, we have the following: ${\left(B_z\right)}_i={\displaystyle \sum _{k=1}^P{\left(B_z\right)}_{i,k}},$ (3) where ${\left(B_z\right)}_i$ is the total magnetic field perturbation that the proton experiences at its i^th position, and $P$ is the total number of MNPs in the simulation (determined by the metal concentration). The proton phase angle evolves over time under the influence of the magnetic field, and its relationship is as follows: ${\psi }_j=\text{Δ}t\cdot \gamma \cdot {\left(B_z\right)}_i,$ (4) where ${\psi }_j$ is the phase angle change of the j^th proton (among many protons from the water molecules in the simulation) during Δt. Then, after the evolvement of the entire echo time (T_E), the final phase angle, ${\text{Φ}}_{j\left(T_E\right)}$, of the j^th proton will also depend on the type of MRI spin-echo pulse sequence. For a single-echo, spin-echo MRI sequence, the phase angle of the proton is inverted 180° (or $\pi$ rad) by the radio pulse only once at time = T_E/2. Thus, we have the following: $\Phi j_{\left(T_{\text{E}}\right)}={\displaystyle \sum _{m=1}^{\frac{T_{\text{E}}}{2\text{Δ}t}}{\psi }_m}-{\displaystyle \sum _{n=\frac{T_{\text{E}}}{2\text{Δ}t}+1}^{\frac{T_{\text{E}}}{\text{Δ}t}}{\psi }_n},$ (5) where m denotes the m^th position in the first half of the proton trajectory, n denotes the n^th position in the second half of the proton trajectory, and $\frac{T_{\text{E}}}{\text{Δ}t}$ is the total number of time steps. For a multi-spin multi-sheet (MSME) MRI sequence, which is often used to accurately determine the r₁ and r₂ of contrast agents, the phase of the proton is inverted 180° by the radio pulses numerous times at $\left(2l+1\right)\cdot {\tau }_{\text{CP}}$, where $l \in Z^{+}$ is a non-negative integer and $2{\tau }_{\text{CP}}$ is the echo spacing between the multiple echoes in the MSME sequence. We thus have the following: $\Phi j_{\left(T_{\text{E}}\right)}={\displaystyle \sum _{\alpha =1}^{\frac{{\tau }_{\text{CP}}}{\text{Δ}t}}{\psi }_{\alpha }}-{\displaystyle \sum _{\beta =\frac{{\tau }_{\text{CP}}}{\text{Δ}t}+1}^{\frac{3{\tau }_{\text{CP}}}{\text{Δ}t}}{\psi }_{\beta }}+ \dots +{\displaystyle \sum _{\zeta =\frac{\left(2l+1\right){\tau }_{\text{CP}}}{\text{Δ}t}+1}^{\frac{T_{\text{E}}}{\text{Δ}t}}{\left(-1\right)}^{l+1}}\cdot {\psi }_{\zeta },$ (6) where α, β, …, and ζ represent each position of the proton trajectory during the first, second, …, and last echo during the T_E time frame. The normalized MRI signal intensity, $\frac{I_{\left(T_{\text{E}}\right)}}{I_0}$, is found as follows: $\frac{I_{\left(T_{\text{E}}\right)}}{I_0}= e^{i\cdot {\Phi }_{j\left(T_{\text{E}}\right)}}=\cos \left[{\Phi }_{j\left(T_{\text{E}}\right)}\right]+i\cdot \sin \left[{\Phi }_{j\left(T_{\text{E}}\right)}\right].$ (7)

In the real space in which our world resides, only the real part of Eq. (7) is observed for the j^th proton (i.e., the projection of the complex vector in Eq. (7) into the real space, which is $\cos \left[{\text{Φ}}_{j\left(T_{\text{E}}\right)}\right]$) [31]. For example, single-loop MRI coils are linearly polarized instead of quadrature. These single-loop MRI coils initially record only a single MR signal channel. However, both in-phase (real) and quadrature (imaginary) channel signals can still be created from this single source by splitting the MR signals into two parts and phase shifting one by 90°. This allows real and imaginary data to be fed into an MRI array processor following the required format for the standard fast Fourier transformation (FFT). Therefore, the modulus of the real-space projection of $\frac{I_{\left(T_{\text{E}}\right)}}{I_0}$, which is defined as ${\left[\frac{I_{\left(T_{\text{E}}\right)}}{I_0}\right]}_{\text{real}}$, is as follows: $\left|{\left[\frac{I_{\left(T_{\text{E}}\right)}}{I_0}\right]}_{\text{real}}\right|=\left|\cos \left[{\Phi }_{j\left(T_{\text{E}}\right)}\right]\right|.$ (8)

To obtain statistically reliable results, we averaged the outcomes from the simulations of many MNP configurations and proton trajectories (i.e., spin trajectories), and obtained the following: $\langle {\left[\frac{I_{\left(T_{\text{E}}\right)}}{I_0}\right]}_{\text{real}}\rangle = \langle \cos \left[{\Phi }_{j\left(T_{\text{E}}\right)}\right]\rangle =\frac{1}{A}{\displaystyle \sum _{h=1}^A\frac{1}{S}}{\displaystyle \sum _{j=1}^S{｛\cos \left[{\Phi }_{j\left(T_{\text{E}}\right)}\right]｝}_h},$ (9) where h denotes the h^th MNP configuration, j denotes the j^th proton, A is the total number of randomized MNP configurations, and S is the total number of randomized spin trajectories. In T₂-weighted (T₂-w) MRI scans, the relationship between the transverse relaxation time (T₂) and observable normalized MRI signal intensity is as follows: $\langle {\left[\frac{{\text{I}}_{\left(T_{\text{E}}\right)}}{{\text{I}}_0}\right]}_{\text{obs}}\rangle =g\cdot e^{-\frac{T_{\text{E}}}{T_2}},$ (10) where g is a constant of proportionality determined by the sensitivity of the signal detection circuit of the MRI scanner. Because transverse relaxation rate R₂ = (T₂)^-1, Eq. (10) can be transformed as follows: $\ln ｛{\left[\frac{{\text{I}}_{\left(T_{\text{E}}\right)}}{{\text{I}}_0}\right]}_{\text{obs}}｝=R_2\cdot T_{\text{E}}-\ln \left(g\right),$ (11)

Because MRI scans are completed in real space, the following is true: $\langle {\left[\frac{{\text{I}}_{\left(T_{\text{E}}\right)}}{{\text{I}}_0}\right]}_{\text{obs}}\rangle =\langle {\left[\frac{I_{\left(T_{\text{E}}\right)}}{I_0}\right]}_{\text{real}} \rangle$. Therefore, after combining Eqs. (9) and (11), if we calculate the $\ln ｛\langle {\left[\frac{{\text{I}}_{\left(T_{\text{E}}\right)}}{{\text{I}}_0}\right]}_{\text{real}}\rangle ｝$ results over multiple MRI echo times (T_E values) and then plot $\ln ｛\langle {\left[\frac{{\text{I}}_{\left(T_E\right)}}{{\text{I}}_0}\right]}_{\text{real}}\rangle ｝$ on the y-axis and $T_{\text{E}}$ on the x-axis, the slope of the linear fit will equal $R_2$, which is our ultimate result, and represents the observable T₂ contrast power of the MNP system for MRI.

Materials and methods

Results and discussion

The framework of the modeling process is shown in Fig.1a, where the configuration of the iron oxide MNPs and the movement trajectory of a proton (the hydrogen nucleus from a water molecule) were randomly generated by MATLAB using a Monte Carlo algorithm. This simulation process needs to be repeated numerous times, and hundreds or even thousands of randomized MNP configurations and proton trajectories should be considered to produce statistically reliable averaged R₂ results [32]. The equation in the inset of Fig. 1a shows how the z-axis component of the magnetic field experienced by the proton (B_z) is calculated in a random scenario (Eqs. (2) and (3)). It can be seen that B_z depends on the root-mean-squared angular frequency shift at the MNP surface (Δω_r, a material-specific quantity) and is particularly sensitive to the MNP radius to its third power ($r_{\text{NP}}^3$).

Fig. 1Full-screen View

(Color online) a) Monte Carlo simulation of the random walk of a proton in the magnetic field perturbation (B_z) generated by magnetic nanoparticles (MNPs). The phase angle of the proton evolves at speed depending on the amplitude of B_z, which is proportional to the cube of the MNP radius (r_NP³) and the root-mean-squared angular frequency shift at the MNP surface (Δω_r). b) Due to different MNP radiuses, a proton will experience varied B_z change speeds near smaller MNPs than larger MNPs. c) The simulated MRI signals at different echo times (T_E) can be linearly fitted to reveal the transversal relaxation rate (R₂) of MNPs. A reduced R₂ will suppress the T₂ effect of MRI, making it better for T₁-w MRI. D) The simulated R₂ values of maghemite and magnetite MNPs range from 1 to 8 nm in diameter, showing that super-small 1 nm -3 nm MNPs are preferred for T₁-w MRI

The high sensitivity of B_z to the MNP radius is illustrated in Fig. 1b, where a smaller MNP generates a smaller magnetic field, depicted by light contour lines, while a larger MNP creates a larger magnetic field, portrayed by dense contour lines. When a proton travels the same movement distance (or for the same time period) around smaller MNPs compared with larger MNPs, the changing speed of the total magnetic field perturbation from MNPs (B_t) caused by small MNPs will be slower. However, because it is the z-axis component, B_z, that affects the MRI signals [37], the changing speed of tilt angle θ must also be considered. Under the same movement distance, the changing speed of tilt angle θ is faster for smaller MNPs than large MNPs, unlike the trend for B_t. Therefore, numerical simulation studies are necessary to determine the behavior of small MNPs. We wrote innovative MATLAB code that utilized the rapid operation of matrices and parallel computing ability, finishing the simulation of several thousand plausible scenarios within a week to obtain Figs. 1c–d. The simulated MRI signals vs. echo times from the two iron oxide MNP diameters (D_NP = 1 and 3 nm) were plotted and linearly fitted in Fig. 1c, where R₂ was the slope of each fitted line. These R₂ values were statistically reliable and satisfied the goodness of fit criterion (>0.99). Because a reduced R₂ suppresses the T₂ effect of MRI and makes it preferred for T₁-w MRI [38], 1-nm iron oxide MNPs (SPIONs) with a lower R₂ were expected to perform better than 3-nm SPIONs in T₁-w MRI. In addition to the SPION diameter, we could vary other SPION structural parameters, such as their crystal type [39, 40]. Figure 1d shows the complete data set of SPIONs with different sizes and crystal types (maghemite: Fe₃O₄ and magnetite: γ-Fe₂O₃). The 1–3-nm SPIONs possessed R₂ values that were roughly five–ten times smaller than the R₂ values of the 6–8-nm SPIONs. Figure 1d also shows that the maghemite SPIONs generally outperformed their magnetite counterparts in T₁-w MRI applications. Overall, the simulation results in Fig. 1 demonstrate that the facile control of SPION structures in modeling simulations can guide the targeted synthesis and characterization of small maghemite SPIONs, saving significant time and materials in experiments.

Because the optimal SPIONs predicted by our Monte Carlo simulations were between 1 and 3 nm in size, we proceeded with the experimental synthesis of 1-, 2-, and 3-nm SPIONs. In the synthetic route shown in Fig. 2a, the Fe(oleate)₃ precursors underwent homogeneous, timed, and temperature-controlled thermal decomposition in tailored solvents. Immediately after synthesis, the oleic acid-coated SPIONs were initially hydrophobic. To make them water-soluble and biocompatible, we performed ligand exchanges with 2-[2-(2-methoxyethoxy)ethoxy]acetic acid (MEAA) and zwitterionic dopamine sulfonate (ZDS) ligands in succession following our established protocols [34]. The TEM images shown in Fig. 2b and 2c confirmed the diameters of the 2- and 3-nm SPIONs and their satisfactory dispersity. Because iron is a light-metal element with moderate contrast under TEM, their extremely small diameters made it difficult to clearly visualize the 1-nm SPIONs; instead, their diameters were confirmed using small-angle X-ray scattering (SAXS) [41]. Moreover, our SQUID measurements compared the magnetizations of the 1-, 2-, and 3-nm SPIONs with commercial MRI contrast agents, including Feraheme^® (6-nm SPION cores) and Magnevist^® (Gd-DTPA). As shown in Figure 2D, the 1-, 2-, and 3-nm SPIONs had lower magnetizations under the same magnetic field strength. Because a low magnetization generally translates to a small r₂ value and suppresses T₂ effects in MRI [42], the 1–3-nm SPIONs are expected to perform better in T₁-w MRI, validating our previous computational predictions. In the enlarged view of Fig. 2d, we quantified the magnetization change (|ΔM_4T→6T|%) percentages of all the magnetic substances and found that the 1-nm SPIONs displayed the strongest unsaturated magnetization among the SPIONs. We calculated the surface metal atomic ratios of all the magnetic substances to further explain this phenomenon, which is usually caused by superficial paramagnetic atoms on SPION surfaces [43]. The results are listed in Table 1, which shows that the 1-nm SPIONs possessed the highest surface ratio (80.2%) among the SPIONs. This was consistent with the fact that they had the strongest unsaturated magnetization (44.7%), as shown in Fig. 2d, and would be beneficial for T₁-w MRI. Therefore, our synthetic and magnetic characterization data aligned with the computational predictions, rendering it more convincing that 1-nm SPION was the most promising candidate for T₁-w MRI applications.

Fig. 2Full-screen View

(Color online) a) Synthetic schematic of 1-, 2-, and 3-nm SPIONs that were predicted by our Monte Carlo simulations to be the optimal SPIONs for T₁-weighted (T₁-w) MRI. b–c) TEM images of 2- and 3-nm SPIONs, where both yellow scale bars denote 20 nm. d) SQUID measurements of 1-, 2-, and 3-nm SPIONs; Feraheme^® (ferumoxytol); and Magnevist^® (gadolinium-diethylenetriamine-penta-acetic acid). The zoomed-in view of d) on the right side shows the magnetization changes of the SPIONs and Magnevist^® from 4 to 6 Tesla (T)

To reveal the relationship between the SPION structures and their magnetic properties, we carefully examined the as-synthesized SPIONs using a combination of XRD and XAFS techniques. In Fig. 3a, it can be observed that all the SPIONs generally matched the three major XRD peaks of the maghemite standard at 2θ = 35.2°, 41.6°, and 63.3°, based on our measurements. Moreover, the SPION XRD peaks were significantly different from the three major XRD peaks for hematite (adopted from the reference [44]) at 2θ = 33.2°, 35.8°, and 49.5°. However, when the SPION diameter decreased from 3 nm to 1 nm, the XRD peaks broadened, and their signal-to-noise ratio also decreased; thus, it became difficult to determine the exact structure of SPIONs smaller than 3 nm. This is because the number of periodic crystal planes diminished with the decrement of nanoparticle diameter [16], leading to a limited number of lattice unit cells within a single SPION and weaker XRD signals. Therefore, we utilized an intense, energy-tunable synchrotron X-ray source [17] to investigate the detailed atomic structure of the 1-nm SPION. The EXAFS full spectra (6900–7800 eV) of the 1-nm SPION and bulk minerals are shown in Figure 3B. Furthermore, based on detailed analyses of the above EXAFS data, the radial distribution functions in Figure 3C showed that the 1-nm SPION was similar to maghemite between 2.0 Å and 3.5 Å but was remarkably different from hematite. Moreover, the XANES results shown in Fig. 3e confirmed the similarity between the 1-nm SPION and maghemite (7135–7150 eV), while validating the difference between the 1-nm SPION and hematite at 7130 eV. Because maghemite is a highly magnetic and stable form of iron oxide minerals [39], the EXAFS and XANES results explained the magnetism of the 1-nm SPIONs. To further unveil the geometry of our 1-nm SPIONs, considering the fact that iron is a light-metal atom and TEM experiments usually struggle to visualize them on a single nanometer scale, we used the FEFF9 software [45] to perform XANES simulations on three representative shapes (Fig. 3d) commonly found in nanoscale synthesis. As shown in Fig. 3f, the overall trend of the nanosphere simulated spectrum was similar to that of the 1-nm SPION experimental XANES in Fig. 3e, and the reasons for this good match were multifold. First, the FEFF9 software uses an ab initio, self-consistent, and real-space multiple scattering approach for rigorous simulation [46], with polarization dependence, core-hole effects, and local field corrections. The FEFF9 calculation also uses an all-electron, real-space, and relativistic Green’s function formalism with no symmetry requirements, leading to a high level of accuracy [47]. Second, multiple sources of experimental evidence, including the results of XRD and XAFS studies, have confirmed that our 1-nm SPION has a maghemite-like structure. Finally, our refined SPION synthesis technique involves the thermal decomposition of the iron precursors at the boiling point of the chosen solvent with ample stirring, ensuring a highly homogeneous reaction temperature throughout the reaction vessel without any temperature gradient. This isotropic and uniform reaction environment naturally leads to a symmetric shape for the SPION products [35, 36], which is spherical. Therefore, the as-proposed maghemite nanosphere represents the geometry of our 1-nm SPIONs, resulting in a sound match between the maghemite nanosphere FEFF9 simulation result and the experimental XANES of the 1-nm SPIONs. Not surprisingly, the simulated spectra of nanocubes and nanorods were generally different from the experimental XANES spectra for the 1-nm SPIONs; in particular, the first white-line peak of the simulated spectrum of the nanocube at 7120 eV (or the simulated spectrum of the nanorod at 7140 eV) significantly differed from the first experimental white-line peak of the 1-nm SPIONs. The XAFS and XRD results of comprehensive structural studies shown in Fig. 3 verified that our SPIONs maintained their maghemite structure and spherical shape even at 1 nm, indicating the capability of our rational synthesis to target a selected SPION conformation and formula.

Fig. 3Full-screen View

(Color online) a) XRD spectra of SPIONs with different sizes compared with bulk iron oxide minerals. The arrows indicate the match between the SPIONs and maghemite. b) The EXAFS spectra of the 1-nm SPION and bulk minerals. The arrows indicate the match between the 1-nm SPIONs and maghemite, while the cross mark points out the difference between the 1-nm SPION and hematite. c) Radial distribution functions of the 1-nm SPION and bulk minerals based on an analysis of the above EXAFS spectra. d) The three representative shapes often found in nanoscale synthesis are shown and were used for simulations: nanosphere (top), nanocube (bottom left), and nanorod (bottom right), where iron is shown in blue and oxygen is shown in red. e) Experimental X-ray near-edge structure (XANES) spectra of 1-nm SPION and bulk iron oxide minerals, where an arrows shows a match and the cross mark shows a difference. f) Simulated XANES spectra of 1-nm maghemite with the three different shapes in d)

To demonstrate the clinical potential of our SPIONs, we evaluated their magnetic resonance (MR) properties using an MRI scanner and compared the results with those of the commercial MRI contrast agents ferumoxytol and Gd-DTPA [36, 48, 49]. In line with our simulation findings, the in vitro MR data in Fig. 4a showed that the T₂ relaxation times of the small SPIONs were higher than those of the larger SPIONs, minimizing the corresponding r₂ relaxivities [r_1,2 = (C_M·T_1,2)^-1 = (T_1,2)^-1, when metal ion concentration C_M = 1 mM in our case]. A lower r₂ relaxivity, in turn, suppresses the T₂ effects in MRI [38], which can be quantified by further considering the r₁ values and calculating the r₁/r₂ ratios, as displayed in Fig. 4b. It can be seen that the r₁/r₂ ratio of our 1-nm SPIONs was 0.91, which even approached the r₁/r₂ ratio of Gd-DTPA, a molecular MRI contrast agent used in clinics [50]. Because the r₁/r₂ ratio is a crucial criterion and elevated r₁/r₂ ratios are desirable for T₁-w MRI [51], our 1-nm SPIONs would be better than the 3-nm SPIONs, ferumoxytol, and other SPION-based contrast agents reported to date [52] for T₁-w MRI applications. Moreover, as illustrated in Fig. 4c, in vivo MRI experiments with mice made it possible to evaluate the in vivo contrast power of the 1-nm SPIONs. The contrast-enhanced MR angiography data in Fig. 4d demonstrated that our 1-nm SPIONs possessed satisfactory T₁ contrast power in vivo, with the ability to highlight major blood vessels and capillaries, along with the heart, kidneys, and bladder. This result also confirmed the kidney clearance of 1-nm SPIONs, an essential pharmacokinetic property in clinical applications to clear unbound SPIONs after the imaging process and reduce potential side effects [53]. The in vitro and in vivo MRI study results shown in Fig. 4 demonstrated the outstanding performance of our 1-nm SPIONs and thus justified the use of a two-pronged computational and experimental strategy for efficient and effective MRI contrast agent development.

Fig. 4Full-screen View

(Color online) a) T₁ and T₂ relaxation times of our 1- and 3-nm SPIONs compared with those of commercial MRI contrast agents (ferumoxytol and Gd-DTPA). The relaxation rate of the dilution component (phosphate-buffered saline) can be neglected. Thus, under moderate metal concentrations, relaxation time T_1,2 (s), relaxation rate R_1,2 (s^-1), and relaxivity r_1,2 (mM^-1·s^-1) have the following relationship: T_1,2 = 1/R_1,2 = 1/(C_M·r_1,2), where C_M is the metal ion concentration (mM). When C_M = 1 mM, T_1,2 = 1/(C_M·r_1,2) = 1/(1·r_1,2) = 1/r_1,2. b) The r₁/r₂ relaxivity ratios of 1- and 3-nm SPIONs, ferumoxytol, and Gd-DTPA. A higher r₁/r₂ ratio is preferred for T₁-w MRI. c) An illustration of the in vitro and in vivo evaluations of SPIONs using an MRI scanner. d) Contrast-enhanced T₁-w MR angiography using the 1-nm SPIONs can highlight the blood vessels, heart, and kidneys of a mouse in vivo

Conclusion

Through MRI simulations in MATLAB, the fundamental mechanisms underlying the contrast power of SPIONs with different structures were revealed, showing that SPIONs with sizes in the range of 1–3 nm were optimal for T₁-weighted MRI. Our experimental synthesis successfully produced the targeted 1–3-nm SPIONs, as confirmed by TEM and SQUID measurements. In particular, XRD and XAFS experiments and analyses revealed that our SPIONs targeted spherical maghemite cores, explaining their magnetic origin. Under in vitro and in vivo MRI conditions, these SPIONs exhibited attractive whole-body contrast power and pharmacokinetic attributes in mice. Overall, these high-performance qualities make our SPIONs promising candidates for MRI and MR angiography applications. This research lays the groundwork for an efficient and robust strategy for the future development and evaluation of nanoparticulate MRI probes. By providing these insights, our two-pronged computational and experimental method has the potential to offer innovative solutions for enhancing diagnostic precision and patient care.