Microcomputed tomography analysis of ferrofluids used as drug carriers for cancer treatment

Two new approaches, Magnetic Drug Targeting (MDT) and Magnetic Hyperthermia, are being investigated in order to reduce side effects generated by common ways of cancer treatment. MDT and MHT are based on the use of magnetic nanoparticles: for MDT the nanoparticles are used as drug carriers and for MHT the nanoparticles are used to induce local heat transfer within the tumour. The success of these therapeutic approaches depends among other things on the correct distribution of the magnetic nanoparticles within the tumour tissue. Computed tomography analysis has been performed on tumour tissue after MDT in order to examine this distribution. The measurements have been performed in two different laboratories, one based on a synchrotron radiation, and another one on a cone X–ray source. First results show that the drug carriers are contained in the vessel system of the tumour as well as concentrated in the surrounding area of the veins. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Investigations of yield stress in ferrofluids with a stress controlled rheometer

One of the most important properties of ferrofluids is the strong change of viscosity when subject to an applied magnetic field – the so called magnetoviscous effect. The rheological experiments as well as theoretical studies correlate this effect with the appearance of chain-like structures of magnetic particles due to the strong interparticle interaction in presence of a magnetic field. Furthermore, viscoelastic effects or other non-Newtonian features, like yield stress in ferrofluids, can theoretically be described with these structures under the influence of the magnetic field. In earlier experiments, when a shear rate controlled rheometer has been used, yield stress could not be investigated directly. A field dependent yield stress could only be estimated in ferrofluids. For direct yield stress investigations, a dedicated stress controlled rheometer is needed, so that the yield stress and its dependence on the magnetic field can be investigated directly. This paper presents investigations of yield stress and its dependence on the magnetic field strength as well as on volume concentration of large magnetic particles. In order to get more information about the structure formed by the particles, variation of gap thickness of the shear cell for the yield stress experiments has been used. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

磁性靶向药物递送中铁磁流体的动力学建模

在所有人体内进行的药物递送技术中,磁性药物靶向递送治疗由于其非入侵性和高靶向性而成为主要的方法．磁性药物靶向递送是将药物装载到磁性纳米颗粒上,利用外部磁场使其移动并聚焦在靶部位的方法．该法能提高靶部位药物的浓度,降低药物对正常组织的毒副作用．尽管已经有不少磁性靶向药物递送的理论分析,但是很少有人研究磁流体在血管里的流体动力学模型．该文提出了一个数学模型来描述作为药物载体的铁磁流体在外磁场作用下,在血管里的流体动力学特性,并在模型中增加了磁场力以及由此产生的不对称应力,增加了磁性纳米颗粒在磁场作用下的角动量方程．由于运动方程的数学复杂性,通过保留数学模型里物理特性最显著项来获得工程近似．用计算流体力学（CFD）进行数值仿真,分析了铁磁流体在一个模拟动脉瘤血管的三维管道里的流动状况,来进一步理解铁磁流体的临床应用．仿真结果和动物实验相一致．分析结果对于磁性靶向药物递送的各种应用提供了可参考的数据．     

The boundary rigidity problem in the presence of a magnetic field

For a compact Riemannian manifold with boundary, endowed with a magnetic potential α, we consider the problem of restoring the metric g and the magnetic potential α from the values of the Mañé action potential between boundary points and the associated linearized problem. We study simple magnetic systems. In this case, knowledge of the Mañé action potential is equivalent to knowledge of the scattering relation on the boundary which maps a starting point and a direction of a magnetic geodesic into its end point and direction. This problem can only be solved up to an isometry and a gauge transformation of α.For the linearized problem, we show injectivity, up to the natural obstruction, under explicit bounds on the curvature and on α. We also show injectivity and stability for g and α in a generic class G including real analytic ones.For the nonlinear problem, we show rigidity for real analytic simple (g,α), rigidity for metrics in a given conformal class, and locally, near any (g,α)∈G. We also show that simple magnetic systems on two-dimensional manifolds are always rigid.     

Simulation of particle dynamics in a rapidly varying viscous flow

A method for the numerical simulation of the dynamics of particles in a rapidly varying viscous flow has been developed and implemented as a software package. The frequency of variations in the fluid velocity is assumed to be such that the nonlinear terms in the equations of motion can be neglected in comparison with the nonstationary terms. The hydrodynamic interaction of the particles is taken into account. The velocities of the particles and their trajectories are computed. It is found that the trajectories of the particles depend substantially on the ratio of their radii. In the case of dipole particles in a rapidly varying external magnetic field, the hydrodynamic interaction is shown to prevent the particles from approaching each other under the influence of dipole-dipole interaction forces.     

Numerical computations of conductivity over agglomerated continuum percolation models

In order to clarify how the percolation theory governs the conductivities in real materials which consist of small conductive particles, e.g., nanoparticles, with random configurations in an insulator, we numerically investigate the conductivities of continuum percolation models consisting of overlapped particles using the finite difference method as a sequel of our previous article [S. Matsutani, Y. Shimosako, Y. Wang, Int. J. Mod. Phys. C 21 (2010) 709–729]. As the previous article showed the shape effect of each particle by handling different aspect ratios of spheroids, in this article we numerically show influences of the agglomeration of the particles on conductivities after we model the agglomerated configuration by employing a simple numerical algorithm which simulate an agglomerated configuration of particles by a natural parameter. We conclude that the dominant agglomeration effect on the conductivities can be interpreted as the size effect of an analyzed region. We also discuss an effect of shape of the agglomerated clusters on its universal property.     

Bifurcations of phase portraits of a Singular Nonlinear Equation of the Second Class

The soliton dynamics is studied using the Frenkel Kontorova (FK) model with non-convex interparticle interactions immersed in a parameterized on-site substrate potential. The case of a deformable substrate potential allows theoretical adaptation of the model to various physical situations. Non-convex interactions in lattice systems lead to a number of interesting phenomena that cannot be produced with linear coupling alone. In the continuum limit for such a model, the particles are governed by a Singular Nonlinear Equation of the Second Class. The dynamical behavior of traveling wave solutions is studied by using the theory of bifurcations of dynamical systems. Under different parametric situations, we give various sufficient conditions leading to the existence of propagating wave solutions or dislocation threshold, highlighting namely that the deformability of the substrate potential plays only a minor role.     

System of interacting particles and nonlinear diffusion reflecting in a domain with sticky boundary

Summary We study a system of particles and the nonlinear McKean-Vlasov diffusion that is its limit for weak interactions in Statistical Mechanics, reflecting in a domain with sticky boundary. The interaction takes place in particular in the sojourn condition. We show existence and uniqueness for the nonlinear martingale problem, by a contraction argument on time-change. Then we construct the system of particles by a limiting procedure, and show propagation of chaos towards the nonlinear diffusion.

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Résumé Nous étudions un système de particules et la diffusion non-linéaire de type McKean-Vlasov qui en est la limite en Mécanique Statistique pour des interactions faibles, en réflexion dans un domaine à bord collant. L'interaction réside en particulier dans la condition de séjour. Nous montrons l'existence et l'unicité pour le problème de martingales non-linéaire, par une méthode de contraction sur le changement de temps. Nous construisons le système de particules en tant que limite en loi, et démontrons la propagation du chaos vers la diffusion non-linéaire.

     

Calibration of a polychromatic CT equipment for biological tissue samples enriched with magnetic nanoparticles.

Micro-computed tomography (µCT) is a widely used imaging technique. Tomography has been used to study the distribution of magnetic nanoparticles within cancerous tissue after minimal-invasive cancer treatments such as magnetic drug targeting and magnetic hyperthermia. But not only the distribution is a relevant factor for the sucess of these therapeutic aproaches. The concentration of the magnetic nanoparticles within the respective tissue is also of great impact. In this paper we present a calibration procedure of a µCT-equipment for biological tissue samples enriched with magnetic nanoparticles developed to enable a semi-quantitative evaluation of 3-dimensional data sets. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Using the tabu search method for the distribution of supplies in a hospital

Two supply delivery systems in a hospital are compared. In order to evaluate the number of carriers required by the new system, an operational research model has been developed and solved by the tabu search method. The results indicate that the new system is better except on weekend days.This work has been achieved while the second author was visiting the Université de Montréal.     

Faxén relations of arbitrary order and their application

Summary For a particle in Stokes flow the relation between the expansion tensors appearing in the perturbation velocity to gradients of the undisturbed (though arbitrary) velocity are called Faxén relations. The expansion tensors themselves turn out to be defined in terms of moments of the stress and velocity distribution, evaluated for any surface completely enclosing the particles. Since these moments vanish if the stress and velocity fields are regular inside the particle the Faxén relations can be used advantageously, if the classical method of reflections for the hydrodynamic interaction between two particles applies, i.e. if the particles are sufficiently far apart. Assuming this to be so for two interacting spheres, a general recursion formula for the expansion tensors of the (j+1)st reflection in terms of expansion tensors of thejth reflection is derived via the Faxén relations. In this way the interaction problem is reduced to a bookkeeping one. This is demonstrated by calculating the friction tensors to the fourth power of the inverse interparticle distance. Furthermore by evaluating the stresslet for a suspension of pair-interacting spheres we obtain an estimate of the suspension viscosity up to quadratic terms in the volume fraction.

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Zusammenfassung Für ein Teilchen in schleichender Strömung werden die Beziehungen zwischen den Entwicklungstensoren der Störgeschwindigkeit zu den Gradienten des ungestörten (aber beliebigen) Geschwindigkeitsfeldes Faxén Relationen genannt. Die Entwicklungstensoren selbst ergeben sich als Momente der Spannungs- und Geschwindigkeitsverteilung, berechnet über irgendeine beliebige Oberfläche, die das Teilchen umschließt. Da diese Momente für jedes Geschwindigkeits- und Spannungsfeld verschwinden, das im Innern des Teilchens regulär ist, können die Faxén Relationen vorteilhaft angewendet werden, wann immer die Reflexions-methode für 2 Teilchen gültig ist, d.h. die Teilchen müssen genügend weit voneinander entfernt sein. Mit Hilfe der Faxén Relationen wird für wechselwirkende Kugeln im letztgenannten Fall eine Rekursionsformel für die Entwicklungstensoren der (j+1)ten Reflexion abgeleitet, die nur von den Entwicklungstensoren derjten Reflexion abhängt. Dadurch braucht man bei dem hydrodynamischen Wechselwirkungsproblem nur noch genau Buch zu führen. Dies wird dadurch demonstriert, daß die Reibungstensoren bis zur vierten Potenz des inversen Kugelabstandes berechnet werden. Indem wir auch das Stresslet in einer Suspension paarweise wechselwirkender Kugeln berechnen, erhalten wir eine Abschätzung der Suspensionsviskosität einschließlich Gliedern quadratisch in der Konzentration.

     

不同大小粒子之间相互作用的直接数值模拟

应用改进的拉格朗日乘子/虚拟区域算法对不同大小的两个圆形粒子在二维方槽中的沉降过程和相互作用进行了直接数值模拟,并进行了实验验证．结果表明不同大小的两个粒子在沉降过程中的相互作用可以描述为追尾、接触、旋转和分离4个过程,只有当两个粒子尺度差异很小时,才会重复进行DKT过程．在两个粒子相互作用的过程中,小粒子的运动受到大粒子的影响更剧烈一些,而相反大粒子运动包括运动轨迹和速度所受到的影响则相对较小．     

Solvable Three-Body Problem and Painlevé Conjectures

For a special choice of the three interparticle coupling constants in the three-body version of a many-body problem in the plane that was recently investigated, the general solution of the equations of motion can be written in closed form (and is remarkably simple). We also discuss another analogous three-body problem and obtain two third-order highly nonlinear autonomous ODEs whose general solutions, we conjecture, are entire. In other words, we conjecture that these ODEs feature (a strong version of) the Painlevé property.     

Equilibrium in quantum systems of particles with magnetic interaction. Fermi and bose statistics

Quantum systems of particles interacting via an effective electromagnetic potential with zero electrostatic component are considered (magnetic interaction). It is assumed that the j th component of the effective potential for n particles equals the partial derivative with respect to the coordinate of the jth particle of “magnetic potential energy” of n particles almost everywhere. The reduced density matrices for small values of the activity are computed in the thermodynamic limit for d-dimensional systems with short-range pair magnetic potentials and for one-dimensional systems with long-range pair magnetic interaction, which is an analog of the interaction of three-dimensional Chern-Simons electrodynamics (“magnetic potential energy” coincides with the one-dimensional Coulomb (electrostatic) potential energy). Institute of Mathematics, Ukrainian Academy of Sciences, Kiev. Published in Ukrainskii Matematicheskii Zhurnal, Vol. 49, No. 5, pp. 691–698, May 1997.     

A new model for the acoustic wake effect in aerosol acoustic agglomeration processes

The acoustic wake effect has been considered the main agglomeration mechanism in the aerosol acoustic agglomeration processes. However, the existing theoretical model for the acoustic wake effect, which was proposed half century ago, is not accurate enough and overestimates the perturbation velocity in the vicinity of particles by as high as approximately 50%. In this paper, a new model for the acoustic wake effect is established, in which an approximate expression is constructed to describe the perturbation velocity. The newly developed model has been verified to be more accurate than the existing model by both theoretical analysis of boundary conditions and computational fluid dynamics simulation. The trajectories of two particles in a horizontal sound field are calculated based on the new model and the existing model. The results show that the new model corrects the range of initial orientation angle for two particles to successfully agglomerate, which was overestimated in the existing model. Moreover, the collision efficiency of two different-sized particles under the acoustic wake effect is found to be larger in the simulation by the new model than that by the existing model. The new model can be used as a reasonably accurate tool not only for calculating the agglomeration of two particles, but also for the numerical simulation of acoustic agglomeration of an aerosol containing a large number of particles due to its low computational cost.     

Magnetic Force Formulae for Magnets at Small Distances

In [7], the magnetic force on subregions of rigid magnetized bodies was studied as a discrete-to-continuum limit. The derived force formula includes a new term, which depends on the underlying crystalline lattice structure ℒ. It originates from contributions of magnetic dipole-dipole interactions of dipole moments close to the boundary of the considered subregion. Further studies of this new term have led to the question of how the magnetic force between two idealized magnets, which are a distance ε > 0 apart, depends on ε as ε → 0. In this article, analytical aspects of this question are discussed, cf. [5], where also numerical experiments are performed. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

两球形颗粒间横向毛细力的格子Boltzmann研究

采用以Shan-Chen多组分模型为基础的格子Boltzmann-伪固体模型对两颗粒间的浮体和浸润横向毛细力展开数值模拟研究,其中流体-固体间的相互作用及颗粒润湿性质在介观层次上采用简单形式得以充分考虑．三维测试表明,与已有理论解相比,成功再现了横向毛细力与颗粒间距的“1/L”关系,并确认了浸润横向毛细力与表面张力间的线性关系．这表明可进一步应用该模型研究横向毛细力作用下的颗粒自聚集等现象.     

Modeling and simulation of the motion of nanoparticles in cylindrical capillaries allowing particle‐to‐wall interactions

The process of transporting nanoparticles at the blood vessels level stumbles upon various physical and physiological obstacles; therefore, a Mathematical modeling will provide a valuable means through which to understand better this complexity. In this paper, we consider the motion of nanoparticles in capillaries having cylindrical shapes (i.e., tubes of finite size). Under the assumption that these particles have spherical shapes, the motion of these particles reduces to the motion of their centers. Under these conditions, we derive the mathematical model, to describe the motion of these centers, from the equilibrium of the gravitational force, the hemodynamic force and the van der Waals interaction forces. We distinguish between the interaction between the particles and the interaction between each particle and the walls of the tube. Assuming that the minimum distance between the particles is large compared with the maximum radius R of the particles and hence neglecting the interactions between the particles, we derive simpler models for each particle taking into account the particles‐to‐wall interactions. At an error of order O(R) or O(R³)(depending if the particles are 'near' or 'very near' to the walls), we show that the horizontal component of each particle's displacement is solution of a nonlinear integral equation that we can solve via the fixed point theory. The vertical components of the displacement are computable in a straightforward manner as soon as the horizontal components are estimated. Finally, we support this theory with several numerical tests. Copyright © 2016 John Wiley & Sons, Ltd.     

Effect of magnetic field on the flow of a fourth order fluid

A study is made of the flow engendered in a semi-infinite expanse of an incompressible non-Newtonian fluid by an infinite rigid plate moving with an arbitrary velocity in its own plane. The fluid is considered to be fourth order and electrically conducting. A magnetic field is applied in the transverse direction to the flow. The nonlinear problem is solved for constant magnetic field analytically using reduction methods as well as numerically and expressions for the velocity field are obtained. Limiting cases of interest can be deduced by choosing suitable parametric values.     

Friction dominated dynamics of interacting particles locally close to a crystallographic lattice

A system of particles, in general d‐dimensional space, that interact by means of pair potentials and adjust their positions according to the gradient flow dynamics induced by the total energy of the system is studied. The case when the range of the interaction is of the same order as the mean interparticle distance is considered. It is also assumed that particles, locally, are located close to some crystallographic lattice. An appropriate system of equations that describes the evolution of macroscopic deformation of the crystallographic lattice, as well as the system that describes the evolution of the main crystallographic directions is derived. Well‐posedness of the derived system is studied as well as the stability of the particle system. Same examples of potentials that yield stable and unstable systems are given. Copyright © 2012 John Wiley & Sons, Ltd.