Distinguishing Nanoparticle Aggregation from Viscosity Changes in MPS/MSB Detection of Biomarkers.

Magnetic particle spectroscopy (MPS) in the Brownian relaxation regime, also termed magnetic spectroscopy of Brownian motion (MSB), can detect and quantitate very low, sub-nanomolar concentrations of molecular biomarkers. MPS/MSB uses the harmonics of the magnetization induced by a small, low-frequency oscillating magnetic field to provide quantitative information about the magnetic nanoparticles' (mNPs') microenvironment. A key application uses antibody-coated mNPs to produce biomarker-mediated aggregation that can be detected using MPS/MSB. However, relaxation changes can also be caused by viscosity changes. To address this challenge, we propose a metric that can distinguish between aggregation and viscosity. Viscosity changes scale the MPS/MSB harmonic ratios with a constant multiplier across all applied field frequencies. The change in viscosity is exactly equal to the multiplier with generality, avoiding the need to understand the signal explicitly. This simple scaling relationship is violated when particles aggregate. Instead, a separate multiplier must be used for each frequency. The standard deviation of the multipliers over frequency defines a metric isolating viscosity (zero standard deviation) from aggregation (non-zero standard deviation). It increases monotonically with biomarker concentration. We modeled aggregation and simulated the MPS/MSB signal changes resulting from aggregation and viscosity changes. MPS/MSB signal changes were also measured experimentally using 100 nm iron-oxide mNPs in solutions with different viscosities (modulated by glycerol concentration) and with different levels of aggregation (modulated by concanavalin A linker concentrations). Experimental and simulation results confirmed that viscosity changes produced small changes in the standard deviation and aggregation produced larger values of standard deviation. This work overcomes a key barrier to using MPS/MSB to detect biomarkers in vivo with variable tissue viscosity.

One-Sided Multidimensional Statistical Significance Testing: A New Method of Calculating the Statistical Significance of Spectra Used to Demonstrate Magnetic Nanoparticle Sensitivity.

Estimating statistical significance of the difference between two spectra or series is a fundamental statistical problem. Multivariate significance tests exist but the limitations preclude their use in many common cases; e.g., one-sided testing, unequal variance and when few repetitions are acquired all of which are required in magnetic spectroscopy of nanoparticle Brownian motion (MSB). We introduce a test, termed the T-S test, that is powerful and exact (exact type I error). It is flexible enough to be one- or two-sided and the one-sided version can specify arbitrary regions where each spectrum should be larger. The T-S test takes the-one or two-sided p-value at each frequency and combines them using Stouffer's method. We evaluated it using simulated spectra and measured MSB spectra. For the single-sided version, mean of the spectrum, A-T, was used as a reference; the T-S test is as powerful when the variance at each frequency is uniform and outperforms when the noise power is not uniform. For the two-sided version, the Hotelling T2 two-sided multivariate test was used as a reference; the two-sided T-S test is only slightly less powerful for large numbers of repetitions and outperforms rather dramatically for small numbers of repetitions. The T-S test was used to estimate the sensitivity of our current MSB spectrometer showing 1 nanogram sensitivity. Using eight repetitions the T-S test allowed 15 pM concentrations of mouse IL-6 to be identified while the mean of the spectra only identified 76 pM.

Poroelastic Mechanical Properties of the Brain Tissue of Normal Pressure Hydrocephalus Patients During Lumbar Drain Treatment Using Intrinsic Actuation MR Elastography.

RATIONALE AND OBJECTIVES: Hydrocephalus (HC) is caused by accumulating cerebrospinal fluid resulting in enlarged ventricles and neurological symptoms. HC can be treated via a shunt in a subset of patients; identifying which individuals will respond through noninvasive imaging would avoid complications from unsuccessful treatments. This preliminary work is a longitudinal study applying MR Elastography (MRE) to HC patients with a focus on normal pressure hydrocephalus (NPH). MATERIALS AND METHODS: Twenty-two ventriculomegaly patients were imaged and subsequently received a lumbar drain placement for cerebrospinal fluid (CSF) drainage. NPH lumbar drain responders and NPH syndrome nonresponders were categorized by clinical presentation. Displacement images were acquired using intrinsic activation (IA) MRE and poroelastic inversion recovered shear stiffness and hydraulic conductivity values. A stable IA-MRE inversion protocol was developed to produce unique solutions for both recovered properties, independent of initial estimates. RESULTS: Property images showed significantly increased shear modulus (p = 0.003 in periventricular region, p = 0.005 in remaining cerebral tissue) and hydraulic conductivity (p = 0.04 in periventricular region) in ventriculomegaly patients compared to healthy volunteers. Baseline MRE imaging did not detect significant differences between NPH lumbar drain responders and NPH syndrome nonresponders; however, MRE time series analysis demonstrated consistent trends in average poroelastic shear modulus values over the course of the lumbar drain process in responders (initial increase, followed by a later decrease) which did not occur in nonresponders. CONCLUSION: These findings are indicative of acute mechanical changes in the brain resulting from CSF drainage in NPH patients.

Poroelasticity as a Model of Soft Tissue Structure: Hydraulic Permeability Reconstruction for Magnetic Resonance Elastography in Silico.

Magnetic Resonance Elastography allows noninvasive visualization of tissue mechanical properties by measuring the displacements resulting from applied stresses, and fitting a mechanical model. Poroelasticity naturally lends itself to describing tissue - a biphasic medium, consisting of both solid and fluid components. This article reviews the theory of poroelasticity, and shows that the spatial distribution of hydraulic permeability, the ease with which the solid matrix permits the flow of fluid under a pressure gradient, can be faithfully reconstructed without spatial priors in simulated environments. The paper describes an in-house MRE computational platform - a multi-mesh, finite element poroelastic solver coupled to an artificial epistemic agent capable of running Bayesian inference to reconstruct inhomogenous model mechanical property images from measured displacement fields. Building on prior work, the domain of convergence for inference is explored, showing that hydraulic permeabilities over several orders of magnitude can be reconstructed given very little prior knowledge of the true spatial distribution.

Identifying in vivo inflammation using magnetic nanoparticle spectra.

We are developing magnetic nanoparticle (NP) methods to characterize inflammation and infection in vivo. Peritoneal infection in C57BL/6 mice was used as a biological model. An intraperitoneal NP injection was followed by measurement of magnetic nanoparticle spectroscopy of Brownian rotation (MSB) spectra taken over time. MSB measures the magnetization of NPs in a low frequency alternating magnetic field. Two groups of three mice were studied; each group had two infected mice and one control with no infection. The raw MSB signal was compared with two derived metrics: the NP relaxation time and number of NPs present in the sensitive volume of the receive coil. A four compartment dynamic model was used to relate those physical properties to the relevant biological processes including phagocytic activity and migration. The relaxation time increased over time for all of the mice as the NPs were absorbed. The NP number decreased over time as the NPs were cleared from the sensitive volume of the receive coil. The composite p-values for all three rate constants were significant: raw signal, 0.0002, relaxation, <10-16 and local NP clearance, <10-16. However, not all the individual mice had significant changes: Only half the infected mice had significantly different rate constants for raw signal reduction. All infected mice had significantly smaller relaxation time constants. All but one of the infected mice had significantly lower rate constants for local clearance. Relaxation is affected by both phagocytic activity, edema and temperature changes and it should be possible to better isolate those effects to more completely characterize inflammation using more advanced MSB methods. The MSB NP signal can be used to identify inflammation in vivo because it has the unique ability to monitor phagocytic absorption through relaxation measurements.

Measuring protein biomarker concentrations using antibody tagged magnetic nanoparticles.

Under physiological conditions biomarker concentrations tend to rise and fall over time e.g. for inflammation. Ex vivo measurements provide a snapshot in time of biomarker concentrations, which is useful, but limited. Approaching real time monitoring of biomarker concentration(s) using a wearable, implantable or injectable in vivo sensor is therefore an appealing target. As an early step towards developing an in vivo biomarker sensor, antibody (AB) tagged magnetic nanoparticles (NPs) are used here to demonstrate the in vitro measurement of ~5 distinct biomarkers with high specificity and sensitivity. In previous work, aptamers were used to target a given biomarker in vitro and generate magnetic clusters that exhibit a characteristic rotational signature quite different from free NPs. Here the method is expanded to detect a much wider range of biomarkers using polyclonal ABs attached to the surface of the NPs. Commercial ABs exist for a wide range of targets allowing accurate and specific concentration measurements for most significant biomarkers. We show sufficient detection sensitivity, using an in-house spectrometer to measure the rotational signatures of the NPs, to assess physiological concentrations of hormones, cytokines and other signaling molecules. Detection limits for biomarkers drawn mainly from pain and inflammation targets were: 10 pM for mouse Granzyme B (mGZM-B), 40 pM for mouse interferon-gamma (mIFN-γ), 7 pM for mouse interleukin-6 (mIL-6), 40 pM for rat interleukin-6 (rIL-6), 40 pM for mouse vascular endothelial growth factor (mVEGF) and 250 pM for rat calcitonin gene related peptide (rCGRP). Much lower detection limits are certainly possible using improved spectrometers and nanoparticles.

Quantification of magnetic nanoparticles by compensating for multiple environment changes simultaneously.

The quantification of magnetic nanoparticles is important for many applications, especially for in vivo biosensing. The magnetization harmonics used in spectroscopy of magnetic nanoparticles can be used to estimate nanoparticle number or weight. However, other effects such as temperature or relaxation time change can also influence the nanoparticle magnetization. Therefore, it is necessary to compensate for these factors when estimating the amount of magnetic nanoparticles. This paper shows through simulation that a two-dimensional scaling method can be used to improve the accuracy of nanoparticle quantification, especially when multiple effects are present which can influence the nanoparticle magnetization. Finally, an experiment was performed on a Magnetic Spectroscopy of Brownian motion (MSB) apparatus to demonstrate this method, and nanoparticle weight was determined with a mean error of 1.3 ng (1.81%).

Nonlinear Inversion MR Elastography With Low-Frequency Actuation.

Magnetic resonance elastography (MRE) has been developed to noninvasively reconstruct mechanical properties for tissue and tissue-like materials over a frequency range of 10 ~200 Hz. In this work, low frequency (1~1.5 Hz) MRE activations were employed to estimate mechanical property distributions of simulated data and experimental phantoms. Nonlinear inversion (NLI) MRE algorithms based on viscoelastic and poroelastic material models were used to solve the inverse problems and recover images of the shear modulus and hydraulic conductivity. Data from a simulated phantom containing an inclusion with property contrast was carried out to study the feasibility of our low frequency actuated approach. To verify the stability of NLI algorithms for low frequency actuation, different levels of synthetic noise were added to the displacement data. Spatial distributions and property values were recovered well for noise level less than 5%. For the presented experimental phantom reconstructions with regularizations, the computed storage moduli from viscoelastic and poroelastic MRE gave similar results. Contrast was detected between inclusions and background in recovered hydraulic conductivity images. Results and findings confirm the feasibility of future in vivo neuroimaging examinations using natural cerebrovascular pulsations at cardiac frequencies, which can eliminate specialized equipment for high frequency actuation.

Concurrent quantification of magnetic nanoparticles temperature and relaxation time.

PURPOSE: The harmonic spectrum of the magnetization of magnetic nanoparticles (MNPs) in the presence of an applied magnetic field can be used to characterize the properties of the microenvironment of the MNPs. The change in temperature and relaxation time has been measured by varying the magnetic field amplitudes or frequency to obtain the harmonic spectrum. However, scaling estimates of temperature or relaxation time are poor if both change simultaneously. In this work, we show that scaling over both the amplitude and frequency of the applied magnetic field allows both the temperature and relaxation to be estimated simultaneously. METHODS: The scaling methods previously used to measure temperature and relaxation times individually have been expanded to two dimensions allowing both parameters to be estimated simultaneously. Samples with different temperature and relaxation times were measured using a magnetic nanoparticle spectrometer to verify this two-dimensional scaling method. Simulations were also carried out for a range of nanoparticle sizes, and the best particle sizes were estimated for this two-dimensional method. RESULTS: The two-dimensional scaling method achieved a mean error of 0.83% for relaxation time by considering the temperature variation as well as relaxation time changes. The temperature and viscosity of the MNPs were measured simultaneously with the mean error of 1.03°C and 0.011 mPas. For monodisperse particles with Brownian relaxation, simulation showed that core radius of 16 nm and hydrodynamic radius of 23 nm had best accuracy for the scaling method. CONCLUSIONS: The two-dimensional scaling method allows both temperature and relaxation time to be estimated simultaneously. The measurement accuracy can be improved by combining information in ratios and phases of the magnetic harmonics of the magnetization and by choosing the optimal particle sizes.

Phantom evaluations of low frequency MR elastography.

Intrinsic activation MR elastography (IA-MRE) is a novel technique which seeks to estimate brain mechanical properties non-invasively and without external mechanical drivers. The method eliminates actuation hardware and patient discomfort while capitalizing on the brain's intrinsic low frequency motion. This study explores low frequency actuation (1 Hz) MR elastography in phantoms and analyzes performance of non-linear inversion (NLI) of viscoelastic and poroelastic mechanical models as a framework for assessing clinical results from IA-MRE. We present results from four gelatin phantoms and report stiffness resolution of 6 mm (two measurement voxels) with a stiffness contrast ratio of 4.21 relative to the background and 9 mm (three measurement voxels) with a lower stiffness contrast ratio of near 1.77. Stiffness edge resolution was also evaluated using edge spread and line spread functions and yielded a stiffness edge response distance of 9 mm. The intraclass correlation coefficient was high (0.93) between mechanical testing and poroelastic estimates, although quantitative agreement was affected by model-data mismatch. Viscoelastic MRE at low frequencies has issues with non-uniqueness due to small inertial forces, and performed worse than poroelastic MRE in terms of inclusion detection and consistency with mechanical testing. These results present the first evaluation of MR elastography using displacement measurements from an actuation frequency less than 5 Hz and support the validity of brain IA-MRE to recover spatially resolved stiffness changes. They provide a baseline of performance in terms of standard metrics for future animal and human brain stiffness studies and analyses based on intrinsic motion.

MR elastography at 1 Hz of gelatin phantoms using 3D or 4D acquisition.

Magnetic Resonance Elastography (MRE) detects induced periodic motions in biological tissues allowing maps of tissue mechanical properties to be derived. In-vivo MRE is commonly performed at frequencies of 30-100 Hz using external actuation, however, using cerebro-vascular pulsation at 1 Hz as a form of intrinsic actuation (IA-MRE) eliminates the need for external motion sources and simplifies data acquisition. In this study a hydraulic actuation system was developed to drive 1 Hz motions in gelatin as a tool for investigating the performance limits of IA-MRE image reconstruction under controlled conditions. Quantitative flow (QFLOW) MR techniques were used to phase encode 1 Hz motions as a function of gradient direction using 3D or 4D acquisition; 4D acquisition was twice as fast and yielded comparable motion field and concomitant image reconstruction results provided the motion signal was sufficiently strong. Per voxel motion noise floor corresponded to a displacement amplitude of about 20-30 µm. Signal to noise ratio (SNR) was 94 ±â€¯17 for 3D and dropped to 69 ±â€¯10 for the faster 4D acquisition, but yielded octahedral shear stress and shear modulus maps of high quality that differed by only about 20% on average. QFLOW measurements in gel phantoms were improved significantly by adding Mn(II) to mimic relaxation rates found in brain. Overall, the hydraulic 1 Hz actuation system when coupled with 4D sequence acquisition produced a fast reliable approach for future IA-MRE phantom evaluation and contrast detail studies needed to benchmark imaging performance.

Phantom evaluations of nonlinear inversion MR elastography.

This study evaluated non-linear inversion MRE (NLI-MRE) based on viscoelastic governing equations to determine its sensitivity to small, low contrast inclusions and interface changes in shear storage modulus and damping ratio. Reconstruction parameters identical to those used in recent in vivo MRE studies of mechanical property variations in small brain structures were applied. NLI-MRE was evaluated on four phantoms with contrast in stiffness and damping ratio. Image contrast to noise ratio was assessed as a function of inclusion diameter and property contrast, and edge and line spread functions were calculated as measures of imaging resolution. Phantoms were constructed from silicone, agar, and tofu materials. Reconstructed property estimates were compared with independent mechanical testing using dynamic mechanical analysis (DMA). The NLI-MRE technique detected inclusions as small as 8 mm with a stiffness contrast as low as 14%. Storage modulus images also showed an interface edge response distance of 11 mm. Damping ratio images distinguished inclusions with a diameter as small as 8 mm, and yielded an interface edge response distance of 10 mm. Property differences relative to DMA tests were in the 15%-20% range in most cases. In this study, NLI-MRE storage modulus estimates resolved the smallest inclusion with the lowest stiffness contrast, and spatial resolution of attenuation parameter images was quantified for the first time. These experiments and image quality metrics establish quantitative guidelines for the accuracy expected in vivo for MRE images of small brain structures, and provide a baseline for evaluating future improvements to the NLI-MRE pipeline.

Evaluating blood clot progression using magnetic particle spectroscopy.

PURPOSE: To evaluate the thrombus maturity noninvasively providing the promise of much earlier and more accurate diagnosis of diseases ranging from stroke to myocardial infarction to deep vein thrombosis. METHODS: Magnetic spectroscopy of nanoparticle Brownian rotation (MSB), a form of magnetic particle spectroscopy sensitive to Brownian rotation of magnetic nanoparticles, was used for the detection and characterization of blood clots. The nanoparticles' relaxation time was quantified by scaling the MSB spectra in frequency to match the spectra from nanoparticles in a reference state. The nanoparticles' relaxation time, in the bound state, was used to characterize the nanoparticle binding to thrombin on the blood clot. The number of nanoparticles bound to the clot was also estimated. Both the relaxation time and the weight of bound nanoparticles were obtained for clots of several ages, reflecting different stages of development and organization. The impact of clot development was explored using functionalized nanoparticles present during clot formation. RESULTS: The relaxation time of the bound nanoparticles decreases for more mature, organized clots. The number of nanoparticles able to bind the clot diminishes quantitatively with clot age. On mature clots, the nanoparticles bind the thrombin on the surface while for developing clots the nanoparticles bind several thrombin molecules or become trapped in the clot matrix during formation. CONCLUSIONS: By estimating the magnetic nanoparticles' relaxation time the clot age and organization can be predicted. The purposed methods are quick and minimally invasive for in vivo applications.

Harmonic phase angles used for nanoparticle sensing.

A series of techniques have been developed to use magnetic nanoparticles as biosensors to characterize their local microenvironment. Two approaches have been used to obtain quantitative information: model based approaches and scaling based approaches. We have favored scaling based approaches, because approximations made in models can lead to limitations in the accuracy. Currently all the scaling approaches use harmonic ratios to retrieve physical parameters like temperature, viscosity and relaxation time. In this work, we showed that the phase angle of the signal at a single harmonic frequency is an alternative to the ratio. The phase angle is nanoparticle density-independent, and can be used to improve sensitivity, enabling us to measure smaller biomedical effects. With the phase angle as an example, we showed that scaling methods are general and do not depend on specific approximations. We showed that the same scaling techniques can be used with both the phase angle and harmonic ratio because they both depend on the same combinations of physical parameters. Using the phase angle improves the precision and using the combination of phase angles and harmonic ratio provides the best precision.

A numerical framework for interstitial fluid pressure imaging in poroelastic MRE.

A numerical framework for interstitial fluid pressure imaging (IFPI) in biphasic materials is investigated based on three-dimensional nonlinear finite element poroelastic inversion. The objective is to reconstruct the time-harmonic pore-pressure field from tissue excitation in addition to the elastic parameters commonly associated with magnetic resonance elastography (MRE). The unknown pressure boundary conditions (PBCs) are estimated using the available full-volume displacement data from MRE. A subzone-based nonlinear inversion (NLI) technique is then used to update mechanical and hydrodynamical properties, given the appropriate subzone PBCs, by solving a pressure forward problem (PFP). The algorithm was evaluated on a single-inclusion phantom in which the elastic property and hydraulic conductivity images were recovered. Pressure field and material property estimates had spatial distributions reflecting their true counterparts in the phantom geometry with RMS errors around 20% for cases with 5% noise, but degraded significantly in both spatial distribution and property values for noise levels > 10%. When both shear moduli and hydraulic conductivity were estimated along with the pressure field, property value error rates were as high as 58%, 85% and 32% for the three quantities, respectively, and their spatial distributions were more distorted. Opportunities for improving the algorithm are discussed.

Blood clot detection using magnetic nanoparticles.

Deep vein thrombosis, the development of blood clots in the peripheral veins, is a very serious, life threatening condition that is prevalent in the elderly. To deliver proper treatment that enhances the survival rate, it is very important to detect thrombi early and at the point of care. We explored the ability of magnetic particle spectroscopy (MSB) to detect thrombus via specific binding of aptamer functionalized magnetic nanoparticles with the blood clot. MSB uses the harmonics produced by nanoparticles in an alternating magnetic field to measure the rotational freedom and, therefore, the bound state of the nanoparticles. The nanoparticles' relaxation time for Brownian rotation increases when bound [A.M. Rauwerdink and J. B. Weaver, Appl. Phys. Lett. 96, 1 (2010)]. The relaxation time can therefore be used to characterize the nanoparticle binding to thrombin in the blood clot. For longer relaxation times, the approach to saturation is more gradual reducing the higher harmonics and the harmonic ratio. The harmonic ratios of nanoparticles conjugated with anti-thrombin aptamers (ATP) decrease significantly over time with blood clot present in the sample medium, compared with nanoparticles without ATP. Moreover, the blood clot removed from the sample medium produced a significant MSB signal, indicating the nanoparticles are immobilized on the clot. Our results show that MSB could be a very useful non-invasive, quick tool to detect blood clots at the point of care so proper treatment can be used to reduce the risks inherent in deep vein thrombosis.

Sensitivity Limits for in vivo ELISA Measurements of Molecular Biomarker Concentrations.

The extremely high sensitivity that has been suggested for magnetic particle imaging has its roots in the unique signal produced by the nanoparticles at the frequencies of the harmonics of the drive field. That sensitivity should be translatable to other methods that utilize magnetic nanoparticle probes, specifically towards magnetic nanoparticle spectroscopy that is used to measure molecular biomarker concentrations for an "in vivo ELISA" assay approach. In this paper, we translate the predicted sensitivity of magnetic particle imaging into a projected sensitivity limit for in vivo ELISA. The simplifying assumptions adopted are: 1) the limiting noise in the detection system is equivalent to the minimum detectable mass of nanoparticles; 2) the nanoparticle's signal arising from Brownian relaxation is completely eliminated by the molecular binding event, which can be accomplished by binding the nanoparticle to something so massive that it can no longer physically rotate and is large enough that Neel relaxation is minimal. Given these assumptions, the equation for the minimum concentration of molecular biomarker we should be able to detect is obtained and the in vivo sensitivity is estimated to be in the attomolar to zeptomolar range. Spectrometer design and nonspecific binding are the technical limitations that need to be overcome to achieve the theoretical limit presented.

Gradient-Based Optimization for Poroelastic and Viscoelastic MR Elastography.

We describe an efficient gradient computation for solving inverse problems arising in magnetic resonance elastography (MRE). The algorithm can be considered as a generalized 'adjoint method' based on a Lagrangian formulation. One requirement for the classic adjoint method is assurance of the self-adjoint property of the stiffness matrix in the elasticity problem. In this paper, we show this property is no longer a necessary condition in our algorithm, but the computational performance can be as efficient as the classic method, which involves only two forward solutions and is independent of the number of parameters to be estimated. The algorithm is developed and implemented in material property reconstructions using poroelastic and viscoelastic modeling. Various gradient- and Hessian-based optimization techniques have been tested on simulation, phantom and in vivo brain data. The numerical results show the feasibility and the efficiency of the proposed scheme for gradient calculation.

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.

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.