# Quantitative 2D Magnetorelaxometry Imaging of Magnetic Nanoparticles Using Optically Pumped Magnetometers

^{1}

^{2}

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Overview of Experimental OPM Setups for MRX Quantification and 2D Imaging

#### 2.2. MRX Excitation Coil Circuit

#### 2.3. OPM

^{3}and the center of the sensitive volume is located 6 mm behind the sensor front.

#### 2.4. Setup and Procedure for MNP Quantification and 1D Reconstruction

^{®}(Schering, Berlin, Germany) MNP was prepared. The MNP with a hydrodynamic diameter of $45\mathrm{n}\mathrm{m}$ show a bimodal core size distribution with peaks at $5\mathrm{n}\mathrm{m}$ and $24\mathrm{n}\mathrm{m}$ [22]. The eight MNP samples with a sample volume of 140 μL and an iron amount ranging from $139.2\mathsf{\mu}\mathrm{g}$ (≈1 mg/cm

^{3}iron concentration) down to 5.8 μg (≈41 μg/cm

^{3}iron concentration) were freeze dried in Mannitol.

#### 2.5. Setup and Procedure for 2D Imaging

^{3}[8].

#### 2.6. MRX Model

#### 2.7. Data Acquisition and Preprocessing

#### 2.8. System Model and Reconstruction

## 3. Results

#### 3.1. OPM

#### 3.2. MNP Quantification

#### 3.3. 1D Reconstruction

#### 3.4. 2D MRX Imaging

## 4. Discussion

## 5. Conclusion and Outlook

## Author Contributions

## Funding

## Conflicts of Interest

## Abbreviations

MOSFET | Metal Oxide Semiconductor Field-Effect Transistor |

MNP | Magnetic nanoparticle |

MRX | Magnetorelaxometry |

MRXI | Magnetorelaxometry imaging |

OPM | Optically pumped magnetometer |

PCB | Printed circuit board |

SERF | Spin-exchange-relaxation-free |

SQUID | Superconducting quantum interference device |

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**Figure 1.**Setup for MNP quantification and quantitative 1D-reconstruction. Schematic representation (

**a**) and photo (

**b**). Simulated magnetic field map (

**c**) for the third (from left to right) activated excitation coil. Please note the logarithmic scaling of the axis.

**Figure 2.**Setup for 2D MRX imaging. Schematic representation (

**a**) and photo (

**b**). Simulated magnetic field map (

**c**) for the activated top-right excitation coil. Please note the logarithmic scaling of the axis.

**Figure 3.**Simplified schematic of the coil driver: constant current source (I1), high voltage MOSFET (M1), TVS diode (D1), current multiplexer relays (K1–K6), and PCB excitation coils (L1–L6).

**Figure 5.**(

**a**) Raw relaxation data, measured with a single OPM for the dilution series. The data within the sensor dead time is not shown. (

**b**) Relaxation amplitude fits with linear regression of iron concentration vs. relaxation amplitude.

**Figure 6.**1D reconstruction: ground truth and reconstruction for each magnetic nanoparticle (MNP) phantom. Point-like MNP phantoms in (

**a**–

**e**) and dilution series phantoms in (

**f**,

**g**).

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**MDPI and ACS Style**

Jaufenthaler, A.; Schier, P.; Middelmann, T.; Liebl, M.; Wiekhorst, F.; Baumgarten, D. Quantitative 2D Magnetorelaxometry Imaging of Magnetic Nanoparticles Using Optically Pumped Magnetometers. *Sensors* **2020**, *20*, 753.
https://doi.org/10.3390/s20030753

**AMA Style**

Jaufenthaler A, Schier P, Middelmann T, Liebl M, Wiekhorst F, Baumgarten D. Quantitative 2D Magnetorelaxometry Imaging of Magnetic Nanoparticles Using Optically Pumped Magnetometers. *Sensors*. 2020; 20(3):753.
https://doi.org/10.3390/s20030753

**Chicago/Turabian Style**

Jaufenthaler, Aaron, Peter Schier, Thomas Middelmann, Maik Liebl, Frank Wiekhorst, and Daniel Baumgarten. 2020. "Quantitative 2D Magnetorelaxometry Imaging of Magnetic Nanoparticles Using Optically Pumped Magnetometers" *Sensors* 20, no. 3: 753.
https://doi.org/10.3390/s20030753