Chondrosarcoma evaluation using hematein-based x-ray staining and high-resolution 3D micro-CT: a feasibility study.

BACKGROUND: Chondrosarcomas are rare malignant bone tumors diagnosed by analyzing radiological images and histology of tissue biopsies and evaluating features such as matrix calcification, cortical destruction, trabecular penetration, and tumor cell entrapment. METHODS: We retrospectively analyzed 16 cartilaginous tumor tissue samples from three patients (51-, 54-, and 70-year-old) diagnosed with a dedifferentiated chondrosarcoma at the femur, a moderately differentiated chondrosarcoma in the pelvis, and a predominantly moderately differentiated chondrosarcoma at the scapula, respectively. We combined a hematein-based x-ray staining with high-resolution three-dimensional (3D) microscopic x-ray computed tomography (micro-CT) for nondestructive 3D tumor assessment and tumor margin evaluation. RESULTS: We detected trabecular entrapment on 3D micro-CT images and followed bone destruction throughout the volume. In addition to staining cell nuclei, hematein-based staining also improved the visualization of the tumor matrix, allowing for the distinction between the tumor and the bone marrow cavity. The hematein-based staining did not interfere with further conventional histology. There was a 5.97 ± 7.17% difference between the relative tumor area measured using micro-CT and histopathology (p = 0.806) (Pearson correlation coefficient r = 0.92, p = 0.009). Signal intensity in the tumor matrix (4.85 ± 2.94) was significantly higher in the stained samples compared to the unstained counterparts (1.92 ± 0.11, p = 0.002). CONCLUSIONS: Using nondestructive 3D micro-CT, the simultaneous visualization of radiological and histopathological features is feasible. RELEVANCE STATEMENT: 3D micro-CT data supports modern radiological and histopathological investigations of human bone tumor specimens. It has the potential for being an integrative part of clinical preoperative diagnostics. KEY POINTS: • Matrix calcifications are a relevant diagnostic feature of bone tumors. • Micro-CT detects all clinically diagnostic relevant features of x-ray-stained chondrosarcoma. • Micro-CT has the potential to be an integrative part of clinical diagnostics.

Nonequilibrium response of magnetic nanoparticles to time-varying magnetic fields: Contributions from Brownian and Néel processes.

Many technical and biomedical applications of magnetic nanoparticles rely on their response to time-varying magnetic fields. While well-established models exist for either immobile or thermally blocked nanoparticles, the intermediate regime where Brownian as well as Néel relaxation occur at the same time is less well explored. Here, we use an efficient model that allows us to study the nonlinear dynamics of individual magnetic nanoparticles in response to different time-varying magnetic fields over a broad range of field parameters, taking into account both relaxation mechanisms. We provide quasiexact solutions for the longitudinal dynamics as well as approximate formulas from dynamic mean-field theory. Our results are relevant, e.g., for magnetorelaxometry, magnetic fluid hyperthermia, and magnetic particle imaging. For these example applications, we show that the ratio of characteristic Brownian to Néel relaxation time can have a profound impact on characteristic response quantities, especially at large field strengths.

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.

Multiparticle collision dynamics for ferrofluids.

Detailed studies of the intriguing field-dependent dynamics and transport properties of confined flowing ferrofluids require efficient mesoscopic simulation methods that account for fluctuating ferrohydrodynamics. Here, we propose such a new mesoscopic model for the dynamics and flow of ferrofluids, where we couple the multi-particle collision dynamics method as a solver for the fluctuating hydrodynamics equations to the stochastic magnetization dynamics of suspended magnetic nanoparticles. This hybrid model is validated by reproducing the magnetoviscous effect in Poiseuille flow, obtaining the rotational viscosity in quantitative agreement with theoretical predictions. We also illustrate the new method for the benchmark problem of flow around a square cylinder. Interestingly, we observe that the length of the recirculation region is increased, whereas the drag coefficient is decreased in ferrofluids when an external magnetic field is applied compared with the field-free case at the same effective Reynolds number. The presence of thermal fluctuations and the flexibility of this particle-based mesoscopic method provide a promising tool to investigate a broad range of flow phenomena of magnetic fluids, and the method could also serve as an efficient way to simulate solvent effects when colloidal particles are immersed in ferrofluids.

Simulating the flow of interacting ferrofluids with multiparticle collision dynamics.

Ferrofluid flow is fascinating since its fluid properties can conveniently be manipulated by external magnetic fields. Novel applications in micro- and nanofluidics as well as in biomedicine have renewed the interest in the flow of colloidal magnetic nanoparticles with a focus on small-scale behavior. Traditional flow simulations of ferrofluids, however, often use simplified constitutive models and do not include fluctuations that are relevant at small scales. Here we address these challenges by proposing a hybrid scheme that combines the multiparticle collision dynamics method for modeling hydrodynamics with Brownian dynamics simulations of a reliable kinetic model describing the microstructure, magnetization dynamics, and resulting stresses. Since both multiparticle collision dynamics and Brownian dynamics are mesoscopic methods that naturally include fluctuations, this hybrid scheme presents a promising alternative to more traditional approaches, also because of the flexibility to model different geometries and modifying the constitutive model. The scheme was tested in several ways. Poiseuille flow was simulated for various model parameters and effective viscosities were determined from the resulting flow profiles. The effective, field-dependent viscosities are found to be in very good agreement with theoretical predictions. We also study Stokes' second flow problem for ferrofluids. For weak amplitudes and low frequencies of the oscillating plate, we find that the velocity profiles are well described by the result for Newtonian fluids at the corresponding, field-dependent viscosity. Furthermore, the time-dependent profiles of the nonequilibrum magnetization component are well approximated by their steady-state values in stationary shear when evaluated with the instantaneous local shear rate. Finally, we also apply our scheme to simulate ferrofluid shear flow over a rough surface. We find characteristic differences in the nonequilibrium magnetization components when the external field is oriented in flow and in a gradient direction.

Dynamics of interacting magnetic nanoparticles: effective behavior from competition between Brownian and Néel relaxation.

The intriguing properties of magnetic nanoparticles have sparked a growing number of theoretical studies as well as practical applications. Here, we provide the first comprehensive study of the influence of interactions on the two main relaxation mechanisms: internal (Néel) and Brownian relaxation. While non-interacting magnetic nanoparticles show Debye behavior with an effective relaxation time, many authors use this model also for the interacting case. Since Néel relaxation is typically a thermally activated process on times scales that are many orders of magnitude larger than the underlying micromagnetic times, we use extensive computer simulations employing a Brownian dynamics/Monte-Carlo algorithm to show that dipolar interactions lead to significant deviations from the Debye behavior. We find that Néel and Brownian relaxation can be considered as independent processes for short enough times until dipolar interactions lead to a coupling of these mechanisms, making the interpretation more difficult. We provide mean-field arguments that describe these short and long-time, effective relaxation times well for weak up to moderate interaction strengths. Our findings about the coupling of Brownian and Néel process and the effective relaxation time provide an important theoretical insight that will have also important consequences for the interpretation of magnetic susceptibility measurements and magnetorelaxometry analysis.

Diffusion-jump model for the combined Brownian and Néel relaxation dynamics of ferrofluids in the presence of external fields and flow.

Relaxation of suspended magnetic nanoparticles occurs via Brownian rotational diffusion of the particle as well as internal magnetization dynamics. The latter is often modeled by the stochastic Landau-Lifshitz equation, but its numerical treatment becomes prohibitively expensive in many practical applications due to a timescale separation between fast, Larmor-type precession and slow, barrier-crossing dynamics. Here, a diffusion-jump model is proposed to take advantage of the timescale separation and to approximate barrier-crossings as thermally activated jump processes that occur alongside rotational diffusion. The predictions of our diffusion-jump model are compared to reference results obtained by solving the stochastic Landau-Lifshitz equation coupled to rotational Brownian motion. Good agreement is found in the regime of high-energy barriers where Néel relaxation can be considered a thermally activated rare event. While many works in the field have neglected Néel relaxation altogether, our approach opens the possibility to efficiently include Néel relaxation also into interacting many-particle models.

Entanglement dynamics at flat surfaces: Investigations using multi-chain molecular dynamics and a single-chain slip-spring model.

The dynamics of an entangled polymer melt confined in a channel by parallel plates is investigated by Molecular Dynamics (MD) simulations of a detailed, multi-chain model. A primitive path analysis predicts that the density of entanglements remains approximately constant throughout the gap and drops to lower values only in the immediate vicinity of the surface. Based on these observations, we propose a coarse-grained, single-chain slip-spring model with a uniform density of slip-spring anchors and slip-links. The slip-spring model is compared to the Kremer-Grest MD bead-spring model via equilibrium correlation functions of chain orientations. Reasonably good agreement between the single-chain model and the detailed multi-chain model is obtained for chain relaxation dynamics, both away from the surface and for chains whose center of mass positions are at a distance from the surface that is less than the bulk chain radius of gyration, without introducing any additional model parameters. Our results suggest that there is no considerable drop in topological interactions for chains in the vicinity of a single flat surface. We infer from the slip-spring model that the experimental plateau modulus of a confined polymer melt may be different to a corresponding unconfined system even if there is no drop in topological interactions for the confined case.

Gas-liquid phase equilibrium of a model Langmuir monolayer captured by a multiscale approach.

The gas-liquid expanded phase transition of a Langmuir monolayer happens at very low surface concentrations which makes this phenomenon extremely expensive to explore in finite three-dimensional (3D) atomistic simulations. Starting with a 3D model reference system of amphiphilic surfactants at a 2D vapor-liquid interface, we apply our recently developed approach (Phys. Chem. Chem. Phys., 2018, 20, 16238) and map the entire system to an effective 2D system of surfactant center-of-masses projected onto the interface plane. The coarse-grained interaction potential obtained via a force-matching scheme from the 3D simulations is then used to predict the 2D gas-liquid phase equilibrium of the corresponding Langmuir monolayer. Monte Carlo simulations in the Gibbs ensemble are performed to calculate areal densities, chemical potentials and surface pressures of the gaseous and liquid coexisting phases within the monolayer. We compare these simulations to the results of a 2D density functional approach based on Weeks-Chandler-Anderson perturbation theory. We furthermore use this approach to determine the density profiles across the equilibrium gas-liquid dividing line and the corresponding line tensions.

Self-assembly of ellipsoidal particles at fluid-fluid interfaces with an empirical pair potential.

Colloidal particles adsorbed at fluid-fluid interfaces interact via mechanisms that can be specific to the presence of interfaces, for instance, lateral capillary interactions induced by nonspherical particles. Capillary interactions are highly relevant for self-assembly and the formation of surface microstructures, however, these are very challenging to model due to the multibody nature of capillary interactions. This work pursues a direct comparison between our computational modelling approach and experimental results on surface microstructures formed by ellipsoidal particles. We begin by investigating the accuracy of using pairwise interactions to describe the multibody capillary interaction by contrasting exact two- and three-particle interaction energies and we find that the pairwise approximation appears reasonable for the experimentally relevant configurations studied. We then develop an empirical pair potential and use it in Monte-Carlo type simulations to efficiently model the structure formation process for relevant particle properties such as aspect ratio, contact angle and surface coverage, and succeed in reproducing our experimental observations where we spread sterically-stabilised ellipsoidal particles onto an oil-air interface at high surface coverage. At lower surface coverages, we find that the self-assembly process falls into the diffusion-limited colloid aggregation universality class.

Effective interaction potentials for model amphiphilic surfactants adsorbed at fluid-fluid interfaces.

Computer simulations are a useful tool to explore the effects of interactions and structure of surfactants on interfacial microstructure and properties. Starting with "molecular-level", three-dimensional reference systems of short amphiphilic surfactants at fluid-fluid interfaces, we here derive effective interaction potentials for the corresponding two-dimensional systems of structureless particles confined to the interface plane. These reference systems are comprised of two immiscible mono atomic fluids (water- and oil-like particles) and nonionic linear amphiphilic surfactants. Our results show that coarse grained interaction potentials are only weakly dependent on surface concentration but their behavior is strongly dependent on surfactant interactions. The coarse grained system preserves the in-plane surfactant center-of-mass pair correlation function at the interface and the results of surface pressure-area isotherms are in a good agreement. This approach can be extended straightforwardly to other types of surfactants at both fluid-fluid and fluid-gas interfaces providing us with an effective pairwise interaction potential for the surfactant monolayer. These effective interactions can be used to explore large-scale self-assembly within the monolayer especially at low surface concentrations where reference simulations are extremely time-consuming.

Magnetic susceptibility, nanorheology, and magnetoviscosity of magnetic nanoparticles in viscoelastic environments.

While magnetic nanoparticles suspended in Newtonian solvents (ferrofluids) have been intensively studied in recent years, the effects of viscoelasticity of the surrounding medium on the nanoparticle dynamics are much less understood. Here we investigate a mesoscopic model for the orientational dynamics of isolated magnetic nanoparticles subject to external fields, viscous and viscoelastic friction, as well as the corresponding random torques. We solve the model analytically in the overdamped limit for weak viscoelasticity. By comparison to Brownian dynamics simulations we establish the limits of validity of the analytical solution. We find that viscoelasticity not only slows down the magnetization relaxation, shifts the peak of the imaginary magnetic susceptibility χ^{″} to lower frequencies, and increases the magnetoviscosity but also leads to nonexponential relaxation and a broadening of χ^{″}. The model we study also allows us to test a recent proposal for using magnetic susceptibility measurements as a nanorheological tool using a variant of the Germant-DiMarzio-Bishop relation. We find for the present model and certain parameter ranges that the relation of the magnetic susceptibility to the shear modulus is satisfied to a good approximation.

Combined Experimental and Simulation Studies of Cross-Linked Polymer Brushes under Shear.

We have studied the effect of cross-linking on the tribological behavior of polymer brushes using a combined experimental and theoretical approach. Tribological and indentation measurements on poly(glycidyl methacrylate) brushes and gels in the presence of dimethylformamide solvent were obtained by means of atomic force microscopy. To complement experiments, we have performed corresponding molecular dynamics (MD) simulations of a generic bead-spring model in the presence of explicit solvent and cross-linkers. Our study shows that cross-linking leads to an increase in friction between polymer brushes and a counter-surface. The coefficient of friction increases with increasing degree of cross-linking and decreases with increasing length of the cross-linker chains. We find that the brush-forming polymer chains in the outer layer play a significant role in reducing friction at the interface.

Transient inhomogeneous flow patterns in supercooled liquids under shear.

Supercooled liquids and other soft glassy systems show characteristic spatial inhomogeneities in their local dynamical properties. Using detailed molecular dynamics simulations, we find that for sufficiently low temperatures and sufficiently high shear rates supercooled liquids also show transient inhomogeneous flow patterns (shear banding) in the start-up of steady shear flow, similar to what has already been observed for many other soft glassy systems. We verify that the onset of transient shear banding coincides quite well with the appearance of a stress overshoot for temperatures in the supercooled regime. We find that the slower bands adapt less well to the imposed deformation and therefore accumulate higher shear stresses compared to the fast bands at comparable local shear rates. Our results also indicate that the shear rates of the fast and slow bands are adjusted such that the local dissipation rate is approximately the same in both bands.

Nuclear Waste Management under Approaching Disaster: A Comparison of Decommissioning Strategies for the German Repository Asse II.

This article compares different strategies for handling low- and medium-level nuclear waste buried in a retired potassium mine in Germany (Asse II) that faces significant risk of uncontrollable brine intrusion and, hence, long-term groundwater contamination. We survey the policy process that has resulted in the identification of three possible so-called decommissioning options: complete backfilling, relocation of the waste to deeper levels in the mine, and retrieval. The selection of a decommissioning strategy must compare expected investment costs with expected social damage costs (economic, environmental, and health damage costs) caused by flooding and subsequent groundwater contamination. We apply a cost minimization approach that accounts for the uncertainty regarding the stability of the rock formation and the risk of an uncontrollable brine intrusion. Since economic and health impacts stretch out into the far future, we examine the impact of different discounting methods and rates. Due to parameter uncertainty, we conduct a sensitivity analysis concerning key assumptions. We find that retrieval, the currently preferred option by policymakers, has the lowest expected social damage costs for low discount rates. However, this advantage is overcompensated by higher expected investment costs. Considering all costs, backfilling is the best option for all discounting scenarios considered.

Time correlation functions in the Lebwohl-Lasher model of liquid crystals.

Time correlation functions in the Lebwohl-Lasher model of nematic liquid crystals are studied using theory and molecular dynamics simulations. In particular, the autocorrelation functions of angular momentum and nematic director fluctuations are calculated in the long-wavelength limit. The constitutive relations for the hydrodynamic currents are derived using a standard procedure based on non-negativity of the entropy production. The continuity equations are then linearized and solved to calculate the correlation functions. We find that the transverse angular momentum fluctuations are coupled to the director fluctuations and are both propagative. The propagative nature of the fluctuations suppresses the anticipated hydrodynamic long-time tails in the single-particle autocorrelation functions. The fluctuations in the isotropic phase are, however, diffusive, leading to t^{-d/2} long-time tails in d spatial dimensions. The Frank elastic constant measured using the time correlation functions are in good agreement with previously reported results.

Influence of Chain Stiffness, Grafting Density and Normal Load on the Tribological and Structural Behavior of Polymer Brushes: A Nonequilibrium-Molecular-Dynamics Study.

We have performed coarse-grained molecular-dynamics simulations on both flexible and semiflexible multi-bead-spring model polymer brushes in the presence of explicit solvent particles, to explore their tribological and structural behaviors. The effect of stiffness and tethering density on equilibrium-brush height is seen to be well reproduced within a Flory-type theory. After discussing the equilibrium behavior of the model brushes, we first study the shearing behavior of flexible chains at different grafting densities covering brush and mushroom regimes. Next, we focus on the effect of chain stiffness on the tribological behavior of polymer brushes. The tribological properties are interpreted by means of the simultaneously recorded density profiles. We find that the friction coefficient decreases with increasing persistence length, both in velocity and separation-dependency studies, over the stiffness range explored in this work.

Anisotropy of magnetoviscous effect in structure-forming ferrofluids.

The magnetoviscous effect, change in viscosity with change in magnetic field strength, and the anisotropy of the magnetoviscous effect, change in viscosity with orientation of magnetic field, have been a focus of interest for four decades. A satisfactory understanding of the microscopic origin of anisotropy of the magnetoviscous effect in magnetic fluids is still a matter of debate and a field of intense research. Here, we present an extensive simulation study to understand the relation between the anisotropy of the magnetoviscous effect and the underlying change in microstructures of ferrofluids. Our results indicate that field-induced chainlike structures respond very differently depending on their orientation relative to the direction of an externally applied shear flow, which leads to a pronounced anisotropy of viscosity. In this work, we focus on three exemplary values of dipolar interaction strengths which correspond to weak, intermediate, and strong interactions between dipolar colloidal particles. We compare our simulation results with an experimental study on cobalt-based ferrofluids as well as with an existing theoretical model called the chain model. A nonmonotonic behavior in the anisotropy of the magnetoviscous effect is observed with increasing dipolar interaction strength and is explained in terms of microstructure formation.

Reply to "Comment on 'Temperature-dependent orientational ordering on a spherical surface modeled with a lattice spin model' ".

In Romano's Comment [Phys. Rev. E 91, 046501 (2015)] on Sec. II of our paper [Phys. Rev. E 90, 022502 (2014)], the author suggests that our findings concerning the nature of the ordering transition of our modified Lebwohl-Lasher model with two-dimensional planar rotators on a planar lattice are inconsistent with known mathematical results. We argue in this Reply that our findings are in fact in agreement with previous mathematical and simulation results and that the criticisms raised by Romano have no impact on the results presented in our paper.