# Enhanced Methods to Estimate the Efficiency of Magnetic Nanoparticles in Imaging

^{1}

^{2}

^{*}

^{†}

## Abstract

**:**

^{TM}R and its fractionated products have been studied for their imaging performances; however, a detailed magnetic characterization in their immobilized state is still lacking. This is particularly important for applications in MPI that require fixation of magnetic nanoparticles with the target cells or tissues. We examine the magnetic properties of immobilized FeraSpin

^{TM}R, its size fractions, and Resovist

^{®}, and use the findings to demonstrate which magnetic properties best predict performance. All samples show some degree of oxidation to hematite, and magnetic interaction between the particles, which impact negatively on image performance of the materials. MRI and MPI performance show a linear dependency on the slope of the magnetization curve, i.e., initial susceptibility, and average blocking temperature. The best performance of particles in immobilized state for MPI is found for particle sizes close to the boundary between superparamagnetic (SP) and magnetically ordered, in which only Néel relaxation is important. Initial susceptibility and bifurcation temperature are the best indicators to predict MRI and MPI performance.

## 1. Introduction

_{3}O

_{4}) has a saturation magnetization (M

_{S}) of 92 Am

^{2}kg

^{−1}, whereas oxidizing the ferrous iron in its structure to ferric iron leads to the formation of either maghemite (γ-Fe

_{2}O

_{3}) with M

_{S}of around 70 Am

^{2}kg

^{−1}, or hematite (α-Fe

_{2}O

_{3}) with M

_{S}of around 0.4 Am

^{2}kg

^{−1}. Particle size plays an important role for a material’s coercivity and susceptibility, i.e., the initial rise in the magnetization curve in an applied field. How long a particle holds its magnetization is governed by the Néel-Arrhenius Equation (1):

_{o}is known as the attempt time with a value on the order of 10

^{−9}to 10

^{−10}s, K is the anisotropy energy, v is particle volume, H

_{C}is the coercivity, M

_{S}is the saturation magnetization, k

_{B}is Boltzmann’s constant, and T is temperature. If the magnetization decays within the time that a measurement is made, it is known as superparamagnetism. Superparamagnetic (SP) particles are homogeneously magnetized but have no coercivity; their magnetization curves can show saturation if their diameter is more than several nanometers. As the volume increases, the anisotropy energy becomes larger than the thermal energy and the particle will have a stable remanent magnetization. The particle is homogeneously magnetized, and this state is known as stable single domain (SD). If particle size further increases, it is no longer energetically favorable for the particle to be homogenously magnetized, and the particle organizes itself into domains to reduces the magnetization energy. As the number of domains increases within a particle, the coercivity decreases, so that a large particle would have no coercivity [9]. The magnetization within each domain organizes itself so that collectively the total energy is minimized, which reduces the magnetization in the absence of an applied field. This is known as multi-domain (MD) state.

_{S}, shape will influence the magnetic properties, because the magnetization prefers to lie along the longest direction of the particle. Therefore, magnetic properties, such as coercivity and in some cases susceptibility, will be strongest along the preferred direction of magnetization, and weakest normal to the preferred direction; the particles display anisotropic behavior. If particles are close enough so that they magnetically interact, interaction plays a role in modulating the effective magnetic particle size, the particle anisotropy and their uniform dispersion. This can lead to a decrease in M

_{S}and coercivity, in which the decrease in coercivity is similar to what one would expect for a multi-domain particle.

_{S}would be the same for all particle sizes above a few nanometers.

^{®}has been used as the standard for comparing the MPI signal strength in terms of harmonic spectra [14,17,18]. Since Resovist is no longer commercially available, efforts focus presently on synthesizing and testing new materials that will yield similar if not better, image quality. FeraSpin

^{TM}R, manufactured by nanoPET Pharma GmbH (Berlin, Germany), is one example of such a product.

_{2}O

_{3}, with a diameter of 5–7 nm, according to which some of these crystallites aggregate to form particles with a larger diameter, such that there is a broader distribution due to these multi-cores [20] (Figure 1). The mean hydrodynamic diameter is 60 nm. A series of different multi-core size fractions have been isolated from FeraSpin R, namely, FeraSpin XS, FeraSpin M and FeraSpin XL, in which each fraction has a narrower multi-core size distribution than the parent material, and a mean hydrodynamic diameter of 15 nm, 35 nm, and 55 nm, respectively (Figure 1a). The magnetic core of FeraSpin XS has been shown from transmission electron microscopy (TEM) to be on the order of the elementary crystallites, with a mean of 5.8 nm, whereas FeraSpin L (not studied here) has larger aggregates with a mean magnetic core size of 33 nm [20]. Therefore, the average particle size of the fractions increases from XS to XL. Although several studies have been made on FeraSpin R and the FeraSpin series in relation to their performance in MPI [17,18,20,21,22,23], this study performs a more detailed magnetic characterization on the immobilized particles. The magnetic properties of the immobilized particles are compared to the magnetic properties and image performance of Resovist. Information on the static magnetic properties is essential, particularly for MPI applications that demands fixation of the MNP to cells and tissues. Results will help to distinguish the dependence of magnetic properties on particle size, and how this contributes to their final performance for MRI and MPI. We are specifically interested in whether the magnetic properties reflect the size of the elementary crystallites that constitutes a multi-core or particle aggregates. Here, aggregation can either be due to clustering of the elementary crystallites of a multi-core or clustering of the multi-core units. This would mean that the effective magnetic particle size can lie between the size of the crystallites to the size of the multi-core itself. Dipolar interaction between individual multi-core particles could lead to an even larger effective particle size, however coating should inhibit the magnetic interactions, so that the effective magnetic particle size is determined by the degree of aggregation of the crystallites (Figure 1b).

## 2. Results

#### 2.1. Magnetic Characterization

#### 2.1.1. Low-Field Susceptibility

_{M}) [32,33], which indicates that all size fractions have undergone some degree of surface oxidation. The Morin transition is not readily apparent for FeraSpin XS, which can be suppressed due to high internal stress in very small particles [34,35]. The absence of a Verwey transition in all samples further indicates that the original Fe

_{3}O

_{4}has experienced some degree of oxidation to γ-Fe

_{2}O

_{3}[36].

#### 2.1.2. Induced Magnetization

_{2}O

_{3}[37], although ultra-fine particles may also prevent saturation due to surface anisotropy [38]. Measurements were repeated on dried samples (data not shown), and there was no observable difference in the hysteresis loop, which supports that the samples are made up largely of particles with SP behavior, and the closed hysteresis loop is not due to physical (Brownian) rotation of the particles during measurement.

_{o}H

_{C}, of 11.7 mT. FeraSpin XS, the smallest multi-core fraction has a very thin magnetic loop at 30 K with µ

_{o}H

_{C}= 1.1 mT. This suggests that an even lower temperature would be needed to block in the magnetic moment of all particles, and may reflect that crystallites show more limited interaction in the smallest particle fraction. FeraSpin M, FeraSpin R, and Resovist have a µ

_{o}H

_{C}= 6.2 mT. The observed difference in µ

_{o}H

_{C}suggests varying degree of aggregation among the elementary crystallites, whereby the degree of aggregation is related to the multi-core diameter.

#### 2.1.3. FORC Analysis

_{o}H

_{b}, while FeraSpin XS has the largest. The difference suggests that there is more relaxation occurring during the measurement in FeraSpin XS compared to FeraSpin XL. The FeraSpin series suggests an increase in the positive shift in the peak interaction field with decreasing average particle size. FeraSpin R and Resovist have the broadest coercivity profiles extending up to 8 mT, indicating a larger fraction of particles with d ≥ 25 nm. Although the elementary crystallite size is the same in all samples, the broader coercivity distribution indicates that there is significant aggregation [12,22,39].

_{2}O

_{3}. The small spread along interaction axis accounts for little interaction among particles in FeraSpin R. FeraSpin M has a unimodal FORC distribution at 50 K with a spread in coercivity up to 50 mT, and a spread along interaction axis from −20 mT to 40 mT (Figure 5b,d). This suggests that there may be more interaction among the multi-cores that results in a larger effective magnetic particle-size. Note, however, the effective particles size is still SP at room temperature. FeraSpin XL shows a unimodal FORC distribution with a plateau in peak coercivity from 7 mT to 13 mT (Figure 5c,d). The coercivity distribution extends to higher fields, which probably arises from the α-Fe

_{2}O

_{3}. The FORC distribution is more contained at the origin, which suggests that the concentration of ordered particles, i.e., according to their effective magnetic size, is higher compared to the other samples. It also has a narrower spread at higher fields along µ

_{o}H

_{b}, which suggests little to no interaction among the multi-cores.

#### 2.1.4. Zero-Field-Cooled and Field-Cooled Magnetization

_{B}) can be defined from the temperature of peak magnetization in the ZFC curve (Figure 6). The temperature at which the first magnetic particles start to block is defined at the bifurcation point (T

_{S}) on the ZFC and FC curves (Table 1). All samples show a wide blocking spectrum except for FeraSpin XS, due to its narrow particle size distribution (Figure 1 and Figure 6). FeraSpin XL has T

_{S}around room temperature, confirming the presence of larger crystallite aggregates that are blocked (Figure 6a). Resovist and FeraSpin R have similar values for T

_{S}(Figure 6b). It should be noted that FeraSpin R has the broadest plateau at T

_{B}, which reflects a broad range of particle sizes, although the average effective magnetic particle size is nearly equal to that of Resovist.

#### 2.1.5. AC Susceptibility

_{B}is close to room temperature. FeraSpin R and Resovist carry two T

_{B}, one at approximately 40 K representing contribution from fine particles and the second around 300 K that is indicative of larger particles. This bimodal distribution has been modeled from measurements of magnetization versus frequency [43]. Because FeraSpin XS and FeraSpin M display χ″ susceptibility characteristic for a unimodal size distribution, the Néel-Brown equation was used to evaluate the pre-factor or attempt time, τ

_{o}. In this case τ

_{o}= 9.9 × 10

^{−132}s for FeraSpin XS. This has no physical meaning, and is interpreted as reflecting interaction in the particle system. FeraSpin M has τ

_{o}= 1.1 × 10

^{−14}s, which is slightly high with respect to the empirically defined range of 10

^{−8}to 10

^{−11}s [44,45], which suggests that interaction may be influencing the magnetic properties to some extent.

#### 2.2. Imaging Performance

_{1}) and spin-spin relaxivity (R

_{2}). Iron-oxide nanoparticles in the SP size range indirectly cause a rise in the image contrast by altering the relaxation times of neighboring protons, and this is characterized by their relaxivities. T2-weighted image performance is expressed in terms of R

_{1}, R

_{2}and R

_{2}/R

_{1}(Table 2) [46]. FeraSpin XL has the highest negative contrast efficacy in MRI (high R2/R1 value) and the fraction FeraSpin XS the least.

## 3. Discussion

_{3}O

_{4}, but a mixture with γ-Fe

_{2}O

_{3}and α-Fe

_{2}O

_{3}, as seen from the Morin transition (Figure 2). A clear relationship can be seen in the lack of magnetic saturation and T

_{B}(Figure 2, Table 1). As discussed above, very fine particles that are on the order of several nanometers may not magnetically saturate, but the presence of the Morin transition, suggests that α-Fe

_{2}O

_{3}, which has a high coercivity, is responsible for the high field contribution to the magnetization. FeraSpin XS, for example, has the smallest T

_{B}, but also the largest contribution of the high coercivity α-Fe

_{2}O

_{3}as seen in the magnetization curves. FeraSpin XL on the other hand has the least contribution from α-Fe

_{2}O

_{3}and the largest TB.

_{3}O

_{4}crystallites, FeraSpin XL has the largest average effective magnetic particles size, based on the average blocking temperature, followed by FeraSpin M, FeraSpin R and Resovist, which have a similar average effective magnetic size, and FeraSpin XS as the smallest particles. This means that although all samples have crystallites of similar size, the effective magnetic particles size follows the same trend as the physical particle size in the FeraSpin fractions [21]. The effective magnetic particle size should be reflected by T

_{S}in the ZFC-FC magnetization curves and T

_{B}in both the ZFC magnetization and AC susceptibility curves, and we find the lowest T

_{S}and T

_{B}for FeraSpin XS and the highest temperatures for FeraSpin XL. It is interesting to note that FeraSpin R has T

_{B}similar to FeraSpin M, but T

_{S}occurs at a higher temperature. This indicates that the average effective magnetic particle size is similar, but FeraSpin R has a broader particle size distribution. We also find that FeraSpin R and Resovist have a bimodal mean effective magnetic particle size distribution, with one part similar to FeraSpin XS and the other more similar to FeraSpin XL [20]. FORC analysis at 30 K, which is below TB for all samples except FeraSpin XS, shows that FeraSpin R and FeraSpin XL have limited interaction between aggregations within the multi-core, whereas FeraSpin M has more particle interaction. This was further verified from the predicted τo for FeraSpin M, although the amount of interaction cannot be large, because χ″ conforms to Néel relaxation (Figure 7).

_{S}(Figure 8b). These correlations show that MRI performance is controlled by the average effective particle size of the magnetic nanoparticles. Ideally particles should have a high susceptibility, which has been noted in other studies [6,7,21,23]. In practice this means that the particles should be slightly under the boundary between SP and SD particle size, because these have the highest susceptibility [48]. Deviation from the linear relationship, however, can arise from (i) inter-particle interactions and agglomeration, which would lead to a larger effective magnetic particle size, (ii) changes in composition, such as oxidation to a less magnetic phase, or (iii) particle shape.

_{S}, obtained from ZFC, and initial susceptibility are both useful in predicting performance for MRI and MPI. T

_{S}may be better suited when the particles have a broad size distribution. In terms of understanding magnetic properties, magnetization curves (hysteresis loops) provide evidence if there is a difference in magnetic composition when comparing samples. In our case, the slope of the magnetization curve in high field reflects the amount of oxidation of the sample from Fe

_{3}O

_{4}to α-Fe

_{2}O. For this reason initial susceptibility reflects not only particle size, but also composition. The FORC diagrams showed that all samples were SP at room temperature, but that the magnetic core size varied as seen from the different coercivity spectra at 30 K. Because the samples remain SP even though there is aggregation of the crystallite, suggests that the size does not exceed the SP-SD boundary. The FORC results at low temperature also suggest that the crystallites self-assemble, such that the lattice structure is aligned, because, except for FeraSpin XS, interaction in the core is not significant. In this case, the aggregated particle magnetic behavior is similar to a single particle with equivalent size [50] Although both ZFC magnetization and AC susceptibility provide information on average blocking temperature, AC susceptibility was able to distinguish bimodal particle size distributions in FeraSpin R and Resovist in contrast to unimodal distributions in FeraSpin M and XS.

## 4. Materials and Methods

^{−1}. A Princeton Measurement Corporation (PCM, now part of Lake Shore Cryogenics, Westerville, OH, USA) vibrating sample magnetometer (VSM, model 3900) at the Laboratory of Natural Magnetism, ETH-Zurich was used to measure induced magnetization as a function of field, FORC curves, and ZFC-FC. Multiple segment hysteresis loops were measured with a field of ±1 T and 100 ms averaging time.

_{a}) back to saturation. Each FORC with its reverse field is described by its magnetization M(H

_{a}, H

_{b}), in which H

_{b}> H

_{a}, and the FORC distribution is obtained by a mixed second derivative:

_{a}, H

_{b}) to (H

_{c}, H

_{b}), where H

_{c}describes the distribution of coercive force, H

_{c}= (H

_{b}− H

_{a})/2, and H

_{u}describes the distribution of local interaction fields, H

_{u}= (H

_{b}+ H

_{a})/2. A series of 140 FORC were made using 1.2 mT field increment and 100 ms averaging time; data were processed with Winklhofer MATLAB code [51]. The reversible and irreversible changes in magnetization have been isolated using the procedure outlined in [52]. Extracting the SP content is based on the method used in [40,52]. This method assumes that for non-interacting SD particles the reversible contribution makes up 50% of the magnetization, which is the case for Fe

_{3}O

_{4}or γ-Fe

_{2}O

_{3}, dominated by shape anisotropy. Peak susceptibility, ∂M/∂H, is then used to gain a semi-quantitative estimate of the SP fraction.

_{LF}and ν

_{HF}, where in which ν

_{HF}> ν

_{LF}, as:

_{HF}= 3 kHz and ν

_{HF}= 100 Hz for all FeraSpin samples, and with ν

_{HF}= 3 kHz and ν

_{HF}= 300 Hz for Resovist.

## 5. Conclusions

_{3}O

_{4}/γ-Fe

_{2}O

_{3}with some degree of aggregation and oxidation to hematite. Both affect only the effective magnetic particle size, as seen from TB. MRI performance can be assessed on a first order from the magnetization curve and TS, whereby the larger the bulk particle size within SP range the better the performance. This holds because magnetite particles on the SP-SD boundary have the highest susceptibility and can easily align in a field. Bifurcation point may be the better parameter for judging performance, because it is less sensitive to changes in composition as is the case of initial susceptibility. The same is valid for MPI performance on SP particles in suspension. Fixing the particles, however, shows that particles close to magnetic ordering, i.e., SD behavior, did not perform as well, because these are dominated by Brownian motion rather than Néel relaxation. Thus, fixation may lead to a state in which the particles undergo magnetic ordering and therefore cannot respond as easily to an applied field. Although a broader study of different magnetic particles would aid in verifying the linear relationship of imaging performance with T

_{S}, our results support that the bifurcation point could be an easy and quick method in quantifying or assessing the efficiency of any new materials for imaging.

## Acknowledgments

## Author Contributions

## Conflicts of Interest

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Sample Availability: Samples from the FeraSpin^{TM}series are available from nanoPET Pharma under www.viscover-online.de. |

**Figure 1.**(

**a**) Log-normal distributions of intensity-weighted hydrodynamic diameter of FeraSpin R, XS, M and XL, respectively as determined from DLS; (

**b**) Schematic diagram illustrating the magnetic single-core-diameter (crystallite), of a multi-core diameter and the hydrodynamic diameter of sample FeraSpin XS versus FeraSpin XL.

**Figure 3.**Magnetization curves for all samples with magnetization normalized by the maximum magnetization, (

**a**) at 300 K, and (

**b**) at 30 K.

**Figure 4.**FORC distributions for (

**a**–

**c**) FeraSpin fractions; (

**d**) FeraSpin R and (

**e**) Resovist. Material name and smoothing factor SF are indicated at the top of each diagram.

**Figure 5.**FORC distributions at 50 K for (

**a**) FeraSpin R, and its fractions; (

**b**) FeraSpin M; and (

**c**) FeraSpin XL; (

**d**) Corresponding coercivity spectra from FORC analysis.

**Figure 6.**Temperature dependent ZFC (dotted)-FC (solid) magnetization curves for (

**a**) FeraSpin fractions; and (

**b**) FeraSpin R and Resovist.

**Figure 7.**Out-of-phase contribution of the AC-susceptibility as a function of temperature at five frequencies compared with Néel relaxation.

**Figure 8.**Relaxivity ratio as a function of (

**a**) the initial slope of the moment normalized magnetization curve, up to 20 mT; and (

**b**) average T

_{S}. In both cases the probability value is <0.05, suggesting >95% significance of the relationship between the variables in the linear regression model of the data set. R-squared is a statistical measure of how close the data are to the fitted regression line (dashed line).

Sample Name | % Fraction of SP Particles (50 K) | % Fraction of SD Particles (50 K) | T_{S} (K) | T_{B} (K) |
---|---|---|---|---|

FeraSpin XS | - | - | 70 | 30 |

FeraSpin M | 31 | 69 | 155 | 140 |

FeraSpin XL | 25 | 75 | ca. 300 | 210 |

FeraSpin R | 34 | 66 | 250 | 150 |

Resovist | - | - | 220 | 90 |

Sample Name | R_{1} ^{1} | R_{2} ^{1} | R_{2}/R_{1} ^{1} | MPI (Suspension) | MPI (Fixed) |
---|---|---|---|---|---|

FeraSpin XS | 13.0 | 49 | 3.8 | 4 | 4 |

FeraSpin M | 9.9 | 117 | 11.2 | 3 | 1 |

FeraSpin XL | 7.9 | 270 | 34.2 | 1 | 2 |

FeraSpin R | 10.0 | 185 | 18.5 | 2 ^{2} | 3 |

Resovist | 9.3 | 174 | 18.7 | 2 ^{2} | NA |

^{1}MRI measurements were made at 1.4 T and 300 K.

^{2}MPI performance by suspended FeraSpin R and Resovist exhibit same harmonic spectrum [22].

© 2017 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

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**MDPI and ACS Style**

Hirt, A.M.; Kumari, M.; Heinke, D.; Kraupner, A.
Enhanced Methods to Estimate the Efficiency of Magnetic Nanoparticles in Imaging. *Molecules* **2017**, *22*, 2204.
https://doi.org/10.3390/molecules22122204

**AMA Style**

Hirt AM, Kumari M, Heinke D, Kraupner A.
Enhanced Methods to Estimate the Efficiency of Magnetic Nanoparticles in Imaging. *Molecules*. 2017; 22(12):2204.
https://doi.org/10.3390/molecules22122204

**Chicago/Turabian Style**

Hirt, Ann M., Monika Kumari, David Heinke, and Alexander Kraupner.
2017. "Enhanced Methods to Estimate the Efficiency of Magnetic Nanoparticles in Imaging" *Molecules* 22, no. 12: 2204.
https://doi.org/10.3390/molecules22122204