Relaxation Of Magnetic Nanoparticles Research Articles

Rational Design of Magnetic Nanoparticles as T1-T2 Dual-Mode MRI Contrast Agents.

Magnetic nanoparticles (MNPs), either paramagnetic or superparamagnetic depending on their composition and size, have been thoroughly studied as magnetic resonance imaging (MRI) contrast agents using in vitro and in vivo biomedical preclinical studies, while some are clinically used. Their magnetic properties responsible in some cases for high magnetization values, together with large surface area-to-volume ratios and the possibility of surface functionalization, have been used in MRI-based diagnostic and theranostics applications. MNPs are usually used as positive (T1) or negative (T2) MRI contrast agents, causing brightening or darkening of selected regions in MRI images, respectively. This review focusses on recent developments and optimization of MNPs containing Gd, Mn, Fe and other lanthanide ions which may function as dual-mode T1-T2 MRI contrast agents (DMCAs). They induce positive or negative contrast in the same MRI scanner upon changing its operational mode between T1-weighted and T2-weighted pulse sequences. The type of contrast they induce depends critically on their r2/r1 relaxivity ratio, which for DMCAs should be in the 2-10 range of values. After briefly discussing the basic principles of paramagnetic relaxation in MNPs, in this review, the basic strategies for the rational design of DMCAs are presented and typical examples are discussed, including in vivo preclinical applications: (1) the use of NPs with a single type of contrast material, Gd- or Mn-based NPs or superparamagnetic NPs with appropriate size and magnetization to provide T2 and T1 contrast; and (2) inclusion of both types of T1 and T2 contrast materials in the same nanoplatform by changing their relative positions.

Field- and concentration-dependent relaxation of magnetic nanoparticles and optimality conditions for magnetic fluid hyperthermia

The field-dependent relaxation dynamics of suspended magnetic nanoparticles continues to present a fascinating topic of basic science that at the same time is highly relevant for several technological and biomedical applications. Renewed interest in the intriguing behavior of magnetic nanoparticles in response to external fields has at least in parts be driven by rapid advances in magnetic fluid hyperthermia research. Although a wealth of experimental, theoretical, and simulation studies have been performed in this field in recent years, several contradictory findings have so far prevented the emergence of a consistent picture. Here, we present a dynamic mean-field theory together with comprehensive computer simulations of a microscopic model system to systematically discuss the influence of several key parameters on the relaxation dynamics, such as steric and dipolar interactions, the external magnetic field strength and frequency, as well as the ratio of Brownian and Néel relaxation time. We also discuss the specific and intrinsic loss power as measures of the efficiency of magnetic fluid heating and discuss optimality conditions in terms of fluid and field parameters. Our results are helpful to reconcile contradictory findings in the literature and provide an important step towards a more consistent understanding. In addition, our findings also help to select experimental conditions that optimize magnetic fluid heating applications.

Magnetic nanoparticle relaxation processes key for medical imaging techniques

Separating Brownian and Néel relaxation mechanisms by timescale using advanced technology.

Nonlinear response of a dilute ferrofluid to an alternating magnetic field

The response of dilute monodisperse ferrofluid to alternating magnetic field is studied theoretically. Brownian rotational relaxation of magnetic nanoparticles is taken into account. Susceptibilities of magnetization harmonics are calculated in a wide range of field amplitudes and frequencies via three common approaches: the Fokker-Planck equation for the one-particle orientation distribution function, the Martsenyuk-Raikher-Shliomis effective field method and the Langevin dynamics simulation which is based on direct numerical integration of particles’ stochastic equations of motion. A comparison of these approaches revealed that all of them are able to describe accurately the behavior of the fundamental magnetization harmonic in a broad range of field parameters. But in the case of high-order harmonics, shortcomings of Langevin dynamics and the effective field method manifest themselves. Due to strong random fluctuations of the system magnetization, Langevin dynamics fails to produce reliable results in the weak-field limit, i.e. when the characteristic magnetic energy scale is lower than the system thermal energy. The Martsenyuk-Raikher-Shliomis equation gives a large systematic error for high-order harmonics if the field period is comparable with (or smaller than) the Brownian relaxation time.

Improving magnetic nanothermometry accuracy through mixing-frequency excitation.

This study proposes a temperature model for the relaxation of magnetic nanoparticles and a phase measurement method under a mixing-frequency excitation field, which can improve the accuracy of temperature measurements in magnetic nanothermometry. According to the Debye-based magnetization model for magnetic nanoparticles, phases at mixing frequencies are used to solve the problem of a delay in the relaxation phase of the magnetic field at a high frequency. This method can improve the signal-to-noise ratio of the response of the magnetic nanoparticles and weaken the phase shift of the detection coils caused by the changes in temperature. The results of experiments show that the proposed method can achieve static temperature measurement error less than 0.1 K and dynamic temperature measurement error less than 0.2 K.

Non-exponential magnetic relaxation in magnetic nanoparticles for hyperthermia

Magnetic nanoparticle based hyperthermia emerged as a potential tool for treating malignant tumours. The efficiency of the method relies heavily on the knowledge of magnetic properties of the samples; in particular, knowledge of the frequency dependent complex magnetic susceptibility is vital to optimize the irradiation conditions and to provide feedback for material science developments. We study the frequency-dependent magnetic susceptibility of an aqueous ferrite suspension for the first time using non-resonant and resonant radiofrequency reflectometry. We identify the optimal measurement conditions using a standard solenoid coil, which is capable of providing the complex magnetic susceptibility up to 150 MHz. The result matches those obtained from a radiofrequency resonator for a few discrete frequencies. The agreement between the two different methods validates our approach. Surprisingly, the dynamic magnetic susceptibility cannot be explained by an exponential magnetic relaxation behavior even when we consider a particle size-dependent distribution of the relaxation parameter.

Magnetic relaxation of magnetic nanoparticles under the influence of shear flow

We investigate the magnetic relaxation behavior of magnetic nanoparticles (MNP) under the influence of shear flow. To this end, we employed magnetorelaxometry (MRX), which is a very sensitive technique to measure the magnetization decay (magnetic relaxation) of MNP after polarizing their magnetic moments in a magnetic field. For the measurements, we developed a fluidic setup to measure the magnetic relaxation of MNP dispersions passing at specific flow rates through a capillary tube inside the magnetizing coil of the MRX device. We observed a decrease of the two characteristic MRX parameters, the relaxation time (up to 60%) and relaxation amplitude (up to 45%), with increasing flow rate (up to 16 ml min−1) compared to the corresponding values measured at zero shear rate. Further, two different regimes of magnetic relaxation behavior under shear flow could be distinguished: for low MNP concentrations the relaxation time was concentration independent, while for higher MNP concentrations an additional increase of relaxation values by about 13% was observed. This is attributed to MNP interparticle interactions. Since dipole–dipole interactions could be ruled out, we concluded that hydrodynamic interactions are the cause for the shear flow MRX behavior in the high MNP concentration regime.

Development of an optical pumped gradiometric system to detect magnetic relaxation of magnetic nanoparticles

The investigation of magnetic nanoparticles for medical and biological applications is relatively recent and steadily growing. When properly functionalized, magnetic nanoparticles (MNPs) can target cancer cells and deliver a drug or heat to these cells. MNPs are being investigated in several applications in medicine such as hyperthermia, magnetic particle imaging, cell separation and magnetofection, in vitro and in vivo alternating current biosusceptibility, T1 and T2 magnetic resonance contrast agents, and magnetorelaxometry. In each of these applications, a specific physical property is measured. Magnetorelaxometry relies on the fact that when MNPs are magnetized they can relax by the Brownian and Néel mechanisms. Both mechanisms depend on the MNP size and for certain conditions can have a faster relaxation through the Brownian, compared to the Néel, mechanism. This can be exploited to target cells. For certain sizes, when an MNP is free to rotate in the biological fluids, they will relax faster than when attached to a cell. This can provide a high contrast for detection of magnetically-labelled cancer cells, making it possible to differentiate normal from cancer tissue. Until very recently SQUIDs were the main detectors employed to measure MNPs, but Optically Pumped Magnetometers (OPM) are now an attractive alternative. OPMs are smaller, do not need liquid helium, and are simpler to operate than SQUIDs. Here, we present the initial steps of the development of an OPM-based instrument to measure relaxation of MNP in vitro.

Design and validation of magnetic particle spectrometer for characterization of magnetic nanoparticle relaxation dynamics.

The design and validation of a magnetic particle spectrometer (MPS) system used to study the linear and nonlinear behavior of magnetic nanoparticle suspensions is presented. The MPS characterizes the suspension dynamic response, both due to relaxation and saturation effects, which depends on the magnetic particles and their environment. The system applies sinusoidal excitation magnetic fields varying in amplitude and frequency and can be configured for linear measurements (1 mT at up to 120 kHz) and nonlinear measurements (50 mT at up to 24 kHz). Time-resolved data acquisition at up to 4 MS/s combined with hardware and software-based signal processing allows for wide-band measurements up to 50 harmonics in nonlinear mode. By cross-calibrating the instrument with a known sample, the instantaneous sample magnetization can be quantitatively reconstructed. Validation of the two MPS modes are performed for iron oxide and cobalt ferrite suspensions, exhibiting Néel and Brownian relaxation, respectively.

Observation of Brownian relaxation of magnetic nanoparticles using HTS SQUID

We analyzed the sensitivity of a separationless immunoassay scheme using functionalized magnetic nanoparticles (MNPs) and a sensitive HTS SQUID magnetometer. The signal of a 100 mu L sample at a concentration of 1 mg/mL and field of 7.5 nT was 20 m Phi(0). This makes it possible for the sensitivity to be within the range of 50 ng/mL at the required time of up to 100 s per a point in the frequency spectrum.

On the Nature of the maximum in the temperature dependence of magnetic liquid susceptibility

The temperature dependence of the real part of complex magnetic susceptibility of magnetic colloid nanosystems based on glycerol and two samples of fine magnetite powder is studied. The results are interpreted with allowance for specific features of the relaxation of magnetic moment of single-domain particles. A possibility of variations in the relaxation of magnetic nanoparticles is considered.

Magnetic nanoparticles colourization by a mixing-frequency method

Brownian and Néel relaxation of magnetic nanoparticles (MNPs) can be characterized by a highly sensitive mixing-frequency method using a search-coil based detection system. The unique magnetic properties of MNPs have been used for biomarkers detection. In this paper, we present a theory and implement an experimental detection scheme using the mixing-frequency method to identify different MNPs simultaneously. A low-frequency sinusoidal magnetic field is applied to saturate the MNPs periodically. A high-frequency sinusoidal magnetic field is then applied to generate mixing-frequency signals that are highly specific to the magnetization of MNPs. The spectra of each MNP can be defined as the complex magnetization of the MNPs over the field frequency. The magnetic spectra of various MNPs and magnetic beads have been characterized and compared. The differences between the MNPs spectra enable us to identify the individual MNPs at the same time. A test has been done to verify the ratio of two different MNPs in mixed samples based on the proposed theory. The experimental results show that the mixing-frequency method is a promising method for MNPs colourization.

Magnetothermoacoustics from magnetic nanoparticles by short bursting or frequency chirped alternating magnetic field: A theoretical feasibility analysis

To propose an alternative method of thermoacoustic wave generation based on heating of magnetic nanoparticles (MNPs) using alternating magnetic field (AMF). The feasibility of thermoacoustic wave generation from MNPs by applying a short-burst of AMF or a frequency-modulated AMF is theoretically analyzed. As the relaxation of MNPs is strongly dependent upon the amplitude and frequency of AMF, either an amplitude modulated, fixed frequency AMF (termed time-domain AMF) or a frequency modulated, constant amplitude AMF (termed frequency-domain AMF) will result in time-varying heat dissipation from MNPs, which has the potential to generate thermoacoustic waves. Following Rosensweig's model of specific power loss of MNPs in a steady-state AMF, the time-resolved heat dissipations of MNPs of superparamagnetic size when exposed to a short bursting of AMF and∕or to a linearly frequency chirped AMF are derived, and the resulted acoustic propagation is presented. Based on experimentally measured temperature-rise characteristics of a superparamagnetic iron-oxide nanoparticle (SPION) matrix in a steady-state AMF of various frequencies, the heat dissipations of the SPION under time-domain and frequency-domain AMF configurations that could have practical utility for thermoacoustic wave generation are estimated. The initial rates of the temperature-rise of the SPION matrix were measured at an iron-weight concentration of 0.8 mg∕ml and an AMF frequency of 88.8 kHz to 1.105 MHz. The measured initial rates of temperature-rise were modeled by Rosensweig's theory, and projected to 10 MHz AMF frequency, at which a 1 μs bursting corresponding to a 1.55 mm axial resolution of acoustic detection could contain 10 complete cycles of AMF oscillation and the power dissipation is approximately 84 times of that at 1 MHz. Exposing the SPION matrix to a 1 μs bursting of AMF at 10 MHz frequency and 100 Oe field intensity would produce a volumetric heat dissipation of 7.7 μJ∕cm(3) over the microsecond duration of the AMF burst. If the SPION matrix is exposed to a 1 ms long AMF train at 100 Oe field intensity that chirps linearly from 1 to 10 MHz, the volumetric heat dissipation produced over each 2π phase change of the AMF oscillation is estimated to increase from 0.15 to 1.1 μJ∕cm(3) within the millisecond duration of the chirping of AMF. The heat dissipations upon SPION (∼1 mg∕ml iron-weight concentration) by a 1 μs bursting of 100 Oe AMF at 10 MHz and a 1 ms train of 100 Oe AMF that chirps linearly from 1 to 10 MHz were estimated to determine the potential of thermal-acoustic wave generation. Although thermoacoustic wave generation from MNPs by time- or frequency-domain AMF applications is predicted, the experimental generation of such a wave remains challenging.

Measurement of Brownian and Néel Relaxation of Magnetic Nanoparticles by a Mixing-Frequency Method

A detection scheme for both Brownian and Neel relaxation of magnetic nanoparticles (MNPs) is demonstrated by a mixing-frequency method in this paper. MNPs are driven into the saturation region by a low-frequency sinusoidal magnetic field. A high-frequency sinusoidal magnetic field is then applied to generate mixing-frequency signals that are highly specific to the Brownian relaxation of MNPs. These highly sensitive mixing-frequency signals from MNPs are picked up by a pair of balanced built-in detection coils. The relationship between MNPs' relaxation time and phase delays of the mixing-frequency signals behind the applied field is derived, and is experimentally verified. Magnetite MNPs with the core diameter of 35 nm are used for the measurement of Brownian relaxation, and Magnetite MNPs with the core diameter of 12 nm are used for the measurement of Neel relaxation. The results show that both Brownian and Neel relaxation depend on the magnetic offset field. This study provides an in-depth understanding of the relaxation mechanisms of MNPs.

Measurement of Brownian Relaxation of Magnetic Nanoparticle by a Multi-Tone Mixing-Frequency Method

A detection scheme for hydrodynamic size distribution of magnetic nanoparticles (MNPs) is demonstrated by a mixing-frequency method in this paper. MNPs are driven into the saturation region by a low frequency sinusoidal magnetic field. A multi-tone high frequency sinusoidal magnetic field is then applied to generate mixing-frequency signals that are highly specific to the Brownian relaxation of MNPs. These highly sensitive mixing-frequency signals from MNPs are picked up by a pair of balanced built-in detection coils. The relation between MNPs' hydrodynamic size distribution and phase delays of the mixing-frequency signals behind the applied field are derived, and are experimentally verified. Iron oxide MNPs with the core diameter of 30 nm are used for the measurement of Brownian relaxation. The results are fitted well with Debye model. This study provides a volume-based magnetic sensing scheme for the real-time measurement of MNPs hydrodynamic size distribution.

Measurement of magnetic nanoparticle relaxation time.

Nanoparticle relaxation time measurements have many applications including characterizing molecular binding, viscosity, heating, and local matrix stiffness. The methods capable of in vivo application are extremely limited. The hypothesis investigated by the authors was that the relaxation time could be measured quantitatively using magnetic spectroscopy of nanoparticle Brownian motion (MSB). The MSB signal (1) reflects the nanoparticle rotational Brownian motion, (2) can be measured from very low nanoparticle concentrations, and (3) is a function of the product of the drive frequency and the relaxation time characterizing Brownian motion. To estimate the relaxation time, the MSB signal was measured at several frequencies. The MSB signal for nanoparticles with altered relaxation time is a scaled version of that for reference nanoparticles with a known relaxation time. The scaling factor linking the altered and reference MSB measurements is the same factor linking the altered and reference relaxation times. The method was tested using glycerol solutions of varying viscosities to obtain continuously variable relaxation times. The measured relaxation time increased with increasing viscosity of the solution in which the nanoparticles resided. The MSB estimated relaxation time matched the calculated relaxation times based on viscosity with 2% average error. MSB can be used to monitor the nanoparticle relaxation time quantitatively through a scale space correlation of the MSB signal as a function of frequency.

Brownian relaxation of magnetic nanoparticles in fluid: the effect of the solvent

The magnetic contribution of the solvent on the RT ac magnetic susceptibility behaviour of Fe3O4 magnetic nanoparticles in solution at different concentrations, is presented and discussed. The room temperature complex susceptibility of the solvent water was studied as a function of several parameters, namely different ac fields, superimposed dc fields, different pHs and temperature: in any case a transition from a diamagnetic behaviour to a paramagnetic one at a characteristic frequency (~4,500 Hz) was observed. These results were compared with the data obtained for other common organic solvents. A dependence of the complex magnetic susceptibility from the polarity of the solvent was observed. The results were discussed in terms of a paramagnetic contribution of polarization to the whole measured susceptibility proportional to the applied frequency. For the real and imaginary susceptibility of water at room temperature, empirical polynomial equations as a function of the frequency were obtained. On the basis of these fits, the observed complex susceptibilities of the different nanoparticles solutions were corrected from the solvent contribution and the results are presented.

Magnetic Relaxation of Magnetic Nanoparticles Dispersed in Solution under High Frequency Magnetic Field

Magnetic nanoparticles are heated by an applied ac magnetic field, which leads to their use as hyperthermia agents, and the applications of magnetic nanoparticles were reported. In this study, the self-heating property of magnetic nanoparticles dispersed in solution was evaluated by measuring hysteresis loop and susceptibility spectra under ac magnetic field.

Real-time measurement of Brownian relaxation of magnetic nanoparticles by a mixing-frequency method

A detection scheme for real-time Brownian relaxation of magnetic nanoparticles (MNPs) is demonstrated by a mixing-frequency method in this paper. MNPs are driven into the saturation region by a low frequency sinusoidal magnetic field. A high frequency sinusoidal magnetic field is then applied to generate mixing-frequency signals that are highly specific to the magnetization of MNPs. These highly sensitive mixing-frequency signals from MNPs are picked up by a pair of balanced built-in detection coils. The phase delays of the mixing-frequency signals behind the applied field are derived, and are experimentally verified. Commercial iron oxide MNPs with the core diameter of 35 nm are used for the measurement of Brownian relaxation. The results are fitted well with Debye model. Then a real-time measurement of the binding process between protein G and its antibody is demonstrated using MNPs as labels. This study provides a volume-based magnetic sensing scheme for the detection of binding kinetics and interaction affinities between biomolecules in real time.

Multiplexed sensing based on Brownian relaxation of magnetic nanoparticles using acompact AC susceptometer

A novel multiplexed sensing scheme based on the measurement of the magneticsusceptibility of the affinity captured target molecules on magnetic nanoparticles in liquidsuspension is proposed. The AC magnetic susceptibility provides a measurement ofBrownian relaxation behavior of biomolecules bound to magnetic nanoparticles (MNPs)that is related to its hydrodynamic size. A room temperature, compact AC susceptometeris designed and developed to measure complex AC magnetic susceptibility of such magneticnanoparticles. The AC susceptometer exhibits high sensitivity in magnetic fields as low as10 µT for1 mg ml−1 concentrationand 5 µl volume, and is fully software programmable. The capability of biological sensing using theproposed scheme has been demonstrated in proof of principle using the binding ofbiotinylated horseradish peroxidase (HRP) to streptavidin-coated MNPs. The proposedtechnique and instrument are readily compatible with lab-on-chip applications forpoint-of-care medical applications.