Daniel B. Reeves

Simulations of magnetic nanoparticle Brownian motion

Magnetic nanoparticles are useful in many medical applications because they interact with biology on a cellular level thus allowing microenvironmental investigation. An enhanced understanding of the dynamics of magnetic particles may lead to advances in imaging directly in magnetic particle imaging or through enhanced MRI contrast and is essential for nanoparticle sensing as in magnetic spectroscopy of Brownian motion. Moreover, therapeutic techniques like hyperthermia require information about particle dynamics for effective, safe, and reliable use in the clinic. To that end, we have developed and validated a stochastic dynamical model of rotating Brownian nanoparticles from a Langevin equation approach. With no field, the relaxation time toward equilibrium matches Einsteins model of Brownian motion. In a static field, the equilibrium magnetization agrees with the Langevin function. For high frequency or low amplitude driving fields, behavior characteristic of the linearized Debye approximation is reproduced. In a higher field regime where magnetic saturation occurs, the magnetization and its harmonics compare well with the effective field model. On another level, the model has been benchmarked against experimental results, successfully demonstrating that harmonics of the magnetization carry enough information to infer environmental parameters like viscosity and temperature.

Molecular sensing with magnetic nanoparticles using magnetic spectroscopy of nanoparticle Brownian motion.

Functionalized magnetic nanoparticles (mNPs) have shown promise in biosensing and other biomedical applications. Here we use functionalized mNPs to develop a highly sensitive, versatile sensing strategy required in practical biological assays and potentially in vivo analysis. We demonstrate a new sensing scheme based on magnetic spectroscopy of nanoparticle Brownian motion (MSB) to quantitatively detect molecular targets. MSB uses the harmonics of oscillating mNPs as a metric for the freedom of rotational motion, thus reflecting the bound state of the mNP. The harmonics can be detected in vivo from nanogram quantities of iron within 5s. Using a streptavidin-biotin binding system, we show that the detection limit of the current MSB technique is lower than 150 pM (0.075 pmole), which is much more sensitive than previously reported techniques based on mNP detection. Using mNPs conjugated with two anti-thrombin DNA aptamers, we show that thrombin can be detected with high sensitivity (4 nM or 2 pmole). A DNA-DNA interaction was also investigated. The results demonstrated that sequence selective DNA detection can be achieved with 100 pM (0.05 pmole) sensitivity. The results of using MSB to sense these interactions, show that the MSB based sensing technique can achieve rapid measurement (within 10s), and is suitable for detecting and quantifying a wide range of biomarkers or analytes. It has the potential to be applied in variety of biomedical applications or diagnostic analyses.

Temperature of the magnetic nanoparticle microenvironment: estimation from relaxation times

Accurate temperature measurements are essential to safe and effective thermal therapies for cancer and other diseases. However, conventional thermometry is challenging so using the heating agents themselves as probes allows for ideal local measurements. Here, we present a new noninvasive method for measuring the temperature of the microenvironment surrounding magnetic nanoparticles from the Brownian relaxation time of nanoparticles. Experimentally, the relaxation time can be determined from the nanoparticle magnetization induced by an alternating magnetic field at various applied frequencies. A previously described method for nanoparticle temperature estimation used a low frequency Langevin function description of magnetic dipoles and varied the excitation field amplitude to estimate the energy state distribution and the corresponding temperature. We show that the new method is more accurate than the previous method at higher applied field frequencies that push the system farther from equilibrium.

Quantification of magnetic nanoparticles with low frequency magnetic fields: compensating for relaxation effects.

Quantifying the number of nanoparticles present in tissue is central to many in vivo and in vitro applications. Magnetic nanoparticles can be detected with high sensitivity both in vivo and in vitro using the harmonics of their magnetization produced in a sinusoidal magnetic field. However, relaxation effects damp the magnetic harmonics rendering them of limited use in quantification. We show that an accurate measure of the number of nanoparticles can be made by correcting for relaxation effects. Correction for relaxation reduced errors of 50% for larger nanoparticles in high relaxation environments to 2%. The result is a method of nanoparticle quantification suitable for in vivo and in vitro applications including histopathology assays, quantitative imaging, drug delivery and thermal therapy preparation.

Toward Localized In Vivo Biomarker Concentration Measurements

We know a great deal about the biochemistry of cells because they can be isolated and studied. The biochemistry of the much more complex in vivo environment is more difficult to study because the only ways to quantitate concentrations is to sacrifice the animal or biopsy the tissue. Either method disrupts the environment profoundly and neither method allows longitudinal studies on the same individual. Methods of measuring chemical concentrations in vivo are very valuable alternatives to sacrificing groups of animals. We are developing microscopic magnetic nanoparticle (mNP) probes to measure the concentration of a selected molecule in vivo. The mNPs are targeted to bind the selected molecule and the resulting reduction in rotational freedom can be quantified remotely using magnetic spectroscopy. The mNPs must be contained in micrometer sized porous shells to keep them from migrating and to protect them from clearance by the immune system. There are two key issues in the development of the probes. First, we demonstrate the ability to measure concentrations in the porous walled alginate probes both in phosphate buffered saline and in blood, which is an excellent surrogate for the complex and challenging in vivo environment. Second, sensitivity is critical because it allows microscopic probes to measure very small concentrations very far away. We report sensitivity measurements on recently introduced technology that has allowed us to improve the sensitivity by two orders of magnitude, a factor of 200 so far.

Combined Néel and Brown rotational Langevin dynamics in magnetic particle imaging, sensing, and therapy

Magnetic nanoparticles have been studied intensely because of their possible uses in biomedical applications. Biosensing using the rotational freedom of particles has been used to detect biomarkers for cancer, hyperthermia therapy has been used to treat tumors, and magnetic particle imaging is a promising new imaging modality that can spatially resolve the concentration of nanoparticles. There are two mechanisms by which the magnetization of a nanoparticle can rotate, a fact that poses a challenge for applications that rely on precisely one mechanism. The challenge is exacerbated by the high sensitivity of the dominant mechanism to applied fields. Here, we demonstrate stochastic Langevin equation simulations for the combined rotation in magnetic nanoparticles exposed to oscillating applied fields typical to these applications to both highlight the existing relevant theory and quantify which mechanism should occur in various parameter ranges.

Magnetic nanoparticles temperature measurements

Magnetic nanoparticles (MNPs) have an ever increasing role in the medical world, particularly in thermal therapies (magnetohypertermia, ablation) for the treatment of cancer. These treatments would benefit of accurate monitoring of the temperature of the MNPs for optimal remedial conditions. It has been shown that the magnetic spectroscopy of nanoparticle Brownian motion (MSB), can be used to measure the temperature of MNPs.

TU‐G‐217A‐07: Magnetic Nanoparticle Quantitation: Compensating for Relaxation Effects

Purpose: Our hypothesis was that the weight of magnetic nanoparticles could be accurately estimated from the magnetic spectroscopy of nanoparticleBrownian motion (MSB) signal. Quantification is critical to bio‐sensing and histology and is becoming more important in medicalimagining. A nanoparticleassay is important in histology and bio‐sensing where antibody targeted magnetic nanoparticles are used to mark specific protein expression. Quantitative imaging of magnetic nanoparticles is also important in applications including hyperthermia and nanoparticledrug delivery. Two factors make quantitative estimates very difficult to achieve: relaxation effects that change the signal produced by each nanoparticle and non‐nanoparticle iron that confuses mass spectroscopy measurements. We introduce a method only sensitive to nanoparticleiron that compensates for relaxation effects that achieves quantitative estimates of the number of magnetic nanoparticles in a sample. Methods: Samples with varying quantities of iron oxide nanoparticles (100 nm mean hydrodynamic diameter) and varying quantities of glycerol were prepared. The samples contained from 1.46 mg to 0.05 mg nanoparticles and from 0% to 27% glycerol. MSB signals were recorded for each sample. The relaxation time was calculated using previously reported methods. The MSB signals were then shifted in frequency to compensate for the change in relaxation time. The scaling of the normalized MSB signal that approximates the reference sample is the weight of nanoparticles present in the sample. The apparatus used was built for 1.5 mL liquid samples; a system for smaller samples would be more sensitive. Results: The RMS percentage error in the weight of nanoparticles was 4.9%. The RMS error in the weight of nanoparticles was 0.018 mg iron. Other sources of iron such as blood did not bias the estimates. Conclusions: The method presented makes accurate MSB estimates of the weight of nanoparticles. Acknowledgement: NIH‐NCI 1U54CA151662‐01 NIH‐NCI 1U54CA151662‐01

Generalized Scaling and the Master Variable for Brownian Magnetic Nanoparticle Dynamics.

Understanding the dynamics of magnetic particles can help to advance several biomedical nanotechnologies. Previously, scaling relationships have been used in magnetic spectroscopy of nanoparticle Brownian motion (MSB) to measure biologically relevant properties (e.g., temperature, viscosity, bound state) surrounding nanoparticles in vivo. Those scaling relationships can be generalized with the introduction of a master variable found from non-dimensionalizing the dynamical Langevin equation. The variable encapsulates the dynamical variables of the surroundings and additionally includes the particles’ size distribution and moment and the applied field’s amplitude and frequency. From an applied perspective, the master variable allows tuning to an optimal MSB biosensing sensitivity range by manipulating both frequency and field amplitude. Calculation of magnetization harmonics in an oscillating applied field is also possible with an approximate closed-form solution in terms of the master variable and a single free parameter.

Nonlinear Nonequilibrium Simulations of Magnetic Nanoparticles

Magnetic nanoparticles are found in computer memory and in futuristic biomedical applications. General models for the particle dynamics are essential to understanding and predicting dynamical behaviors in diverse conditions. Many approaches have been used to varying degrees of success. Here we present the most general methods for modeling: nonlinear, nonequilibrium models that typically require computational solving. We maintain rigor throughout so that the expressions arise from as close to first principles calculations as possible. We present the intuitively simpler, conceptually satisfying models too but are clear on their ranges of validity. We are also explicit in the computational implementation where necessary. At the end, we summarize the state of the art and the interesting problems that remain unsolved.