Magnetorelaxometry assisting biomedical applications of magnetic nanoparticles

Abstract

Due to their biocompatibility and small size, iron oxide magnetic nanoparticles (MNP) can be guided to virtually every biological environment. MNP are susceptible to external magnetic fields and can thus be used for transport of drugs and genes, for heat generation in magnetic hyperthermia or for contrast enhancement in magnetic resonance imaging of biological tissue. At the same time, their magnetic properties allow one to develop sensitive and specific measurement methods to non-invasively detect MNP, to quantify MNP distribution in tissue and to determine their binding state. In this article, we review the application of magnetorelaxometry (MRX) for MNP detection. The underlying physical properties of MNP responsible for the generation of the MRX signal with its characteristic parameters of relaxation amplitude and relaxation time are described. Existing single and multi-channel MRX devices are reviewed. Finally, we thoroughly describe some applications of MRX to cellular MNP quantification, MNP organ distribution and MNP-based binding assays. Providing specific MNP signals, a detection limit down to a few nanogram MNP, in-vivo capability in conscious animals and measurement times of a few seconds, MRX is a valuable tool to improve the application of MNP for diagnostic and therapeutic purposes.

Fig. 1

Logarithmic 2D plot of the effective relaxation time combining Néel (abscissa, Eq. 4) and Brownian relaxation (ordinate, Eq. 5) according to Eq. 6. Furthermore, the corresponding core and hydrodynamic diameter are displayed for magnetite MNP with an effective anisotropy K ~ 10⁴ J/m³. The straight lines have been added to show the influence of a fixed shell thickness of 5 nm (white line), 10 nm (red line) or a fixed hydrodynamic diameter of 150 nm (orange line) and 160 nm (black line) on the relaxation time with increasing core diameter.

Fig. 2

Effective relaxation time calculated by Eqs. (4–6) for different magnetic core diameters d _p as a function of the hydrodynamic diameter d _h for K _eff = 10⁴ J/m³, T = 290 K and η = 10⁻³ Pa·s. The shaded area is accessible by our MRX setup (10⁻⁴ s to 10² s), as determined by SQUID electronics dead time, sampling frequency and relaxation measurement interval. The green line indicates particles without a nonmagnetic shell layer where d _h = d _p. Immobilized particles are detectable only if they have a core diameter d _p of about 16 nm to 22 nm. If both Brownian and Néel relaxation are present, particles with d _p larger than 16 nm and at the same time d _h in the range from 50 nm to 5 μm are detectable by MRX. For particles with d _p ≥ 23 nm, only Brownian relaxation can be observed in the given time interval.

Fig. 3

Magnetorelaxometry principle. The top line (from left to right) portrays a nanoparticle ensemble‘s behavior: initially in a disordered state without magnetization, partly rotated towards the field direction during magnetizing, and turning back into a randomly oriented distribution of magnetic moments leading to the detected magnetization relaxation. Typically a field of about 1.5 mT is applied for 1 s. After removal of the field and a short interval the SQUID amplifier needs to recover, the relaxation signals are acquired for 0.5 s.

Fig. 4

Magnetorelaxometry devices: a) single channel device, the inset draft shows the centre part of the system with the 150 μl sample container in the magnetizing coil about 12 mm below the SQUID sensor in the Dewar flask. b) 18 channel MRX scanner with integrated superconducting shield. The relaxation of samples and animals up to rabbit size are measured by circumferentially arranged 18 SQUID sensors (inset shows the sensor support chain) located midway of the horizontal warm bore. c) The PTB 304 channel vector magnetometer, the combination of this conventional biomagnetic measurement system operated inside a magnetically shielded room with a d) large Helmholtz coil system (d = 84 cm, located in front of the shielded room) allows MRX measurements on samples up to human size.

Fig. 5

Quantifying the MNP amount of a small tissue sample by single channel MRX. (a) Relaxation curves of the sample piece together with immobilized and fluid MNP reference signals. An arbitrary constant offset B _ofs has been added to the relaxation curves solely for graphical representation. The blue dotted (fluid) and the green dashed (immobilized) curves are the reference signals normalized to match the sample curve. The normalization factor directly is proportional to the iron amount in the sample. (b) Determining the centre of a MNP accumulation in an irregularly shaped tissue sample by double MRX measurement reversing the sample. (c) Individual relaxation curves of an irregularly shaped pig lung sample (inset picture) containing MNP. Together with the relaxation curves of the sample measured in normal (dotted red curve) and upside down (dashed green) orientation the distance corrected relaxation curve (straight black) is displayed.

Fig. 6

Single channel MRX on dissected samples for quantitative reconstruction of a MNP distribution after magnetic aerosol targeting in a pig lung lobe (part. caudalis dorsalis, numbers indicate μg iron/g tissue. (a) MRX quantification results of each tissue piece normalized to tissue mass. (b) Reconstruction of the nanoparticle distribution superimposed onto a picture of the (intact) lung lobe.

Fig. 7

Multi channel MRX of a point-like MNP reference sample. Left) Relaxation curves (57 B _z-sensors) and corresponding magnetic field patterns at t = 5 s, 45 s, 80 s. Right) Decay of magnetic moments (m _x,m _y,m _z) of the MNP determined by Levenberg-Marquardt fitting and analytically for m _z from the magnetic field pattern.

Fig. 8

304ch-MRX quantification of a magnetic nanoparticle accumulation in a conscious mouse: a) the relaxation curve detection by the central SQUID sensor starts some 10 s after switching off the magnetizing field and transporting the conscious mouse housed in a plastic tube beneath the MRX device. Magnetic field pattern snapshots (top row) at time points t = 16 s, 19 s, 24 s, 71 s, 86 s display the point-like dipolar character of a nanoparticle accumulation moving relatively to the sensor positions. Fitting the field patterns for each point in time with the magnetic point dipole model Eq. 13 allows b) the identification of the spatial movement of the mouse and c) the detection of magnetic moment relaxation of the nanoparticles. For comparison the results for a fixed reference sample is added

Fig. 9

Different kinds of MNP based binding-assays for biomolecule detection by MRX: (a) solid phase, (b) liquid phase, (c) bead based, (d) agglutination assay