Cross-calibration of X-ray µCT and MRX for tissue analysis

Ferrofluids are being considered as an aid for local cancer treatments, such as Magnetic Drug Targeting (MDT) and Magnetic Hyperthermia (MHT). Both methods make use of the strong influence of a magnetic field on the nanoparticles, with the aim of treating the cancer locally while reducing, or even eliminating, the side effects that usually occur during conventional cancer treatments. Microcomputed tomography analysis has been performed on tumour tissue after MDT and MHT in order to examine the distribution of the magnetic nanoparticles within the tissue. The majority of the measurements has been performed in a laboratory based on a polychromatic X-ray source. The strong energy dependence of the attenuation coefficient and the occurrence of the so called beam hardening artefacts make the quantitative evaluation of data acquired with polychromatic tomography equipment very difficult. In this paper we present a cross-calibration method for magnetorelaxometry and polychromatic X-ray tomography for biological tissue samples enriched with magnetic nanoparticles. (© 2009 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．     

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)     

Inclusion of interactions in mathematical modelling of implant assisted magnetic drug targeting

Drug delivery technologies are an important area within biomedicine. Targeted drug delivery aims to reduce the undesired side effects of drug usage by directing or capturing the active agents near a desired site within the body. This is particularly beneficial in, for instance, cancer chemotherapy, where the side effects of general (systemic) drug administration can be severe.One approach to targeted drug delivery uses magnetic nanoparticles as the constituents of carriers for the desired active agent. Once injected into the body, the behaviour of these magnetic carriers can be influenced and controlled by magnetic fields. In implant assisted magnetic drug targeting systems a magnetic implant, typically a stent, wire or spherical seed can be used to target sites deep within the body as the implant acts as a focus for the resulting magnetic force. This can be easily understood as the force depends on the gradient of the magnetic field and the gradient near the implant is large.In designing such a system many factors need to be considered including physical factors such as the size and nature of the implants and carriers, and the fields required. Moreover, the range of applicability of these systems in terms of the regions of the vasculature system, from low blood velocity environments, such as capillary beds to higher velocity arteries, must be considered. Furthermore, assessment criteria for these systems are needed. Mathematical modelling and simulation has a valuable role to play in informing in vitro and in vivo experiments, leading to practical system design.Specifically, the implant assisted magnetic drug targeting systems of Avilés, Ebner and Ritter are considered within this review, and two dimensional mathematical modelling is performed using the open source C++ finite volume library OpenFOAM. In the first system treated, a large ferromagnetic particle is implanted into a capillary bed as a seed to aid collection of single domain nanoparticles (radius 20-100 nm). The Langevin function is used to calculate the magnetic moment of the particles, and the model is further adapted to treat the agglomeration of particles known to occur in these systems. This agglomeration can be attributed to interparticle interactions and here the magnetic dipole-dipole and hydrodynamic interactions for two mutually interacting nanoparticles are modelled, following Mikkelsen et al. who treated two particle interactions in microfluidic systems, with low magnetic field (0.05 T). The resulting predicted performance is found to both increase and decrease significantly depending on initial positions of the particles. Secondly, a ferromagnetic, coiled wire stent is implanted in a large arterial vessel. The magnetic dipole-dipole and hydrodynamic interactions for multiple particles are included. Different initial positions are considered and the system performance is assessed. Inclusion of these interactions yields predictions that are in closer agreement with the experimental results of Avilés et al. We conclude that the discrepancies between the non interacting theoretical predictions and the corresponding experimental results can (as suggested by Avilés et al.) be largely attributed to interparticle interactions and the consequent agglomeration.     

Reconstruction of biologic tissue conductivity from noisy magnetic field by integral equation method

Magnetic resonance electrical impedance tomography (MREIT) is a new technique to recover the conductivity of biologic tissue from the induced magnetic flux density. This paper proposes an inversion scheme for recovering the conductivity from one component of the magnetic field based on the nonlinear integral equation method. To apply magnetic fields corresponding to two incoherent injected currents, an alternative iteration scheme is proposed to update the conductivity. For each magnetic field, the regularizing technique on the finite dimensional space is applied to solve an ill-posed linear system. Compared with the well-developed harmonic B_z method, the advantage of this inversion scheme is its stability, since no differential operation is required on the noisy magnetic field. Numerical implementations are given to show the convergence of the iteration and its validity for noisy input data.     

Continuum-Mechanical Analysis of Human Brain Tissue

The effective treatment of brain diseases, such as malignant brain tumours, is generally constricted by the controlled contribution of therapeutic agents. Novel brain tumour therapy proceeds from a direct infusion of the drug into the extra-vascular space of the nervous brain tissue (convection-enhanced delivery). This is carried out using catheter to bypass the blood-brain barrier, which effectively separates brain tissue from the intra-vascular space and hence hamper drug delivery through the bloodstream. The dilation of the target tissue, as response to the local pressure increase, initiates interstitial fluid flow and, thus, the distribution of the chemical agents. An adequate constitutive model of the complex tissue aggregate in the framework of the Theory of Porous Media is essential in order to assist modern clinical application via numerical simulations. The presented model consists of an elastically deformable solid skeleton, provided by the tissue cells, permeated by two viscous, materially incompressible pore-liquid phases, interstitial fluid and blood plasma. Both liquids are mobile within the solid skeleton and separated from each other. With regard to simulate a drug infusion process in the extra-vascular space, the interstitial fluid is treated as a solution of a liquid solvent and a dissolved therapeutic solute. The constitutive assumptions for the involved constituents are adjusted in order to describe the physical behaviour of human brain tissue. The presented numerical examples illustrate the fundamental effects during an infusion process. Therefore, the resulting set of coupled partial differential equations is spatially discretised using hexahedral mixed finite elements with an implicit (backward) Euler time integration scheme to solve the considered problem in a monolithic manner for the primary variables. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Mathematical modeling and simulation of the earth's magnetic field: A comparative study of the models on the spacecraft attitude control application

In this paper, the Earth's magnetic field models which are widely used in spacecraft attitude control applications are modeled and extensively compared with a reference model. The reference model is obtained utilizing coefficients from the last generation of International Geomagnetic Reference Field (IGRF-12). The validity of this model is verified with the World Magnetic Model (WMM) in terms of intensity and direction of the field. The reference model is then used to evaluate lower-order and approximating models while the influence of effective parameters such as expansion order of modeling, orbit height, inclination, latitude and longitude on accuracy of modeling is investigated. The simulation results for several scenarios are presented and discussed. The linear and nonlinear transformations of the models from orbital frame to spacecraft body frame are compared for a wide range of attitude angles in order to investigate the sensibility and validity of linear transformation. Simulation of a spacecraft attitude control maneuver is performed to demonstrate the importance of the accuracy of the magnetic field model which is implemented in the attitude control system. The results indicated a meaningful increase in control effort when a simplified model was used. This research was aimed to investigate the borders of different geomagnetic field models and transformations for spacecraft attitude control applications. The presented results may lead to a proper choice of the Earth's magnetic field model based on the space mission requirements.     

Two variants of magnetic diffusivity stabilized finite element methods for the magnetic induction equation

We consider the time‐dependent magnetic induction model where the sought magnetic field interacts with a prescribed velocity field. This coupling results in an additional force term and time dependence in Maxwell's equation. We propose two different magnetic diffusivity stabilized continuous nodal‐based finite element methods for this problem. The first formulation simply adds artificial magnetic diffusivity to the partial differential equation, whereas the second one uses a local projected magnetic diffusivity as stabilization. We describe those methods and analyze them semi‐discretized in space to get bounds on stabilization parameters where we distinguish equal‐order elements and Taylor‐Hood elements. Different numerical experiments are performed to illustrate our theoretical findings.     

Computational complexity analysis for multiple hypothesis tracking

This paper presents a detailed analysis of computational complexity of Multiple Hypothesis Tracking (MHT). The result proves that the computational complexity of MHT is dominated by the number of hypotheses. Effects of track merging and pruning are analyzed also. Certain common design parameters of MHT, such as thresholds, are also discussed in detail. The results of this paper provide a guidance for selecting parameters in an MHT tracker and predicting its performance.Among the design parameters discussed in this paper, track merging appears to be the most important way for controlling the computational complexity of MHT. Thresholds for track deletion are also critical. If not all measurements are allowed to initiate new tracks, the number of new tracks can also be used for tuning the computation requirement of MHT, but it is not as significant as thresholds.     

Magnetic structure of Pr6Fe13Ge studied by M(o)ssbauer effect and neutron diffraction

Magnetic structure of Pr6Fe13Ge at room temperature has been investigated by magnetic measurement, M ssbauer effect and neutron diffraction. Magnetic atoms are closely packed up and down the mirror planes at z=0 and 1/2 and separated by the non-magnetic atoms located on the planes at z=1/4 and 3/4, which constructs an M/NM/M sandwich structure (M: magnetic, NM: non-magnetic). The intralayer magnetic moments couple ferromagnetically and are out of ab plane at a small angle so as to form a component along c-axis. The interlayer coupling is antiferromagnetic for the ab component while ferromagnetic for the c component.     

矩形永磁体磁场分布的解析表达式

从分子环流模型出发,利用毕奥-萨伐尔定理,对于仅在一个方向均匀完全充磁的矩形永磁块体,导出了其外部空间磁场分布的解析表达式．该解析式能精确描述一块至多块按极性相反并列放置时矩形永磁体外部空间的磁场分布．针对单块永磁体,还分析了磁场分布与永磁体几何尺寸之间的依赖关系,以及磁场大小随外部空间点离开永磁体表面距离之间的关系;定量分析了横向磁场的强度均匀度和分布均匀度随永磁体几何尺寸和离开永磁体表面距离的变化规律．     

Lie symmetry group analysis of magnetic field effects on free convective flow of a nanofluid over a semi-infinite stretching sheet

We investigate the steady two-dimensional flow of an incompressible water based nanofluid over a linearly semi-infinite stretching sheet in the presence of magnetic field numerically. The basic boundary layer equations for momentum and heat transfer are non-linear partial differential equations. Lie symmetry group transformations are used to convert the boundary layer equations into non-linear ordinary differential equations. The dimensionless governing equations for this investigation are solved numerically using Nachtsheim–Swigert shooting iteration technique together with fourth order Runge–Kutta integration scheme. Effects of the nanoparticle volume fraction ϕ, magnetic parameter M, Prandtl number Pr on the velocity and the temperature profiles are presented graphically and examined for different metallic and non-metallic nanoparticles. The skin friction coefficient and the local Nusselt number are also discussed for different nanoparticles.     

Three-dimensional mathematical modelling of magnetic bead interactions within a magnetic separation system

Magnetic separation relates to the ability to separate particles based on their magnetic mobilities. This is often limited by the formation of bead agglomerates. Bead agglomerates are formed as a result of attractive magnetic induced interactions among magnetic beads suspended in fluid. A three-dimensional model of the interactions among three equal sized super-paramagnetic beads suspended in a static fluid within a uniform magnetic field is presented here. The beads’ trajectories were recorded on video while the relative axial displacement of the bead was obtained using the recorded off-focus images. A good agreement was obtained by comparing the beads’ simulated trajectories with the video data. Therefore, the model is able to predict the behaviour of magnetic beads in immunoassays as well as magnetic separation system.     

Modeling and analysis of an auction-based logistics market

We consider a logistics spot market where the transportation orders from a number of firms are matched with two types of carriers through a reverse auction. In the spot market, local carriers compete with in-transit carriers that have lower costs. In order to analyze the effects of implementing a logistics spot market on these three parties: firms, local carriers, and in-transit carriers and also the effects of various system parameters, we develop a two-stage stochastic model. We first model the auction in a static setting and determine the expected auction price based on the number of carriers engaging in the auction and their cost distributions. We then develop a continuous-time Markov chain model to evaluate the performance of the system in a dynamic setting with random arrivals and possible abandonment of orders and carriers. By combining these two models, we evaluate the performance measures such as the expected auction price, price paid to the carriers, distribution of orders between local and in-transit carriers, and expected number of carriers and orders waiting at the logistics center in the long run. We present analytical and computational results related to the performance of the system and discuss operation of such a logistics spot market in Turkey.     

Comparison between two common collocation approaches based on radial basis functions for the case of heat transfer equations arising in porous medium

In this paper two common collocation approaches based on radial basis functions have been considered; one be computed through the integration process (IRBF) and one be computed through the differentiation process (DRBF). We investigated the two approaches on natural convection heat transfer equations embedded in porous medium which are of great importance in the design of canisters for nuclear wastes disposal. Numerical results show that the IRBF be performed much better than the common DRBF, and show good accuracy and high rate of convergence of IRBF process.     

New estimating equation approaches with application in lifetime data analysis

Estimating equation approaches have been widely used in statistics inference. Important examples of estimating equations are the likelihood equations. Since its introduction by Sir R. A. Fisher almost a century ago, maximum likelihood estimation (MLE) is still the most popular estimation method used for fitting probability distribution to data, including fitting lifetime distributions with censored data. However, MLE may produce substantial bias and even fail to obtain valid confidence intervals when data size is not large enough or there is censoring data. In this paper, based on nonlinear combinations of order statistics, we propose new estimation equation approaches for a class of probability distributions, which are particularly effective for skewed distributions with small sample sizes and censored data. The proposed approaches may possess a number of attractive properties such as consistency, sufficiency and uniqueness. Asymptotic normality of these new estimators is derived. The construction of new estimation equations and their numerical performance under different censored schemes are detailed via Weibull distribution and generalized exponential distribution.     

EXPONENTIAL MESH APPROXIMATIONS FOR A 3D EXTERIOR PROBLEM IN MAGNETIC INDUCTION

A numerical method combining the approaches of C.I. Goldstein and L.-A. Ying is used for the simulation in three-dimensional magnetostatics related to an exterior problem in magnetic induction. Recently introduced, this method is based on the use of a graded mesh obtained by gluing homothetic layers in the exterior domain and has been performed in the case of edge element discretizations. In this work, the theoretical and practical aspects of the method are inspected in the case of face element and volume element discretizations,for computing a magnetic induction. Error estimates, implementations, and numerical results are provided.     

Effect of mass transfer and diffusion of nanofluid on the thermal ablation of malignant cells during magnetic hyperthermia

Malignant cells can be ablated by a specific treatment temperature during magnetic hyperthermia, which is induced by the power dissipation of magnetic nanoparticles (MNPs) inside tumor region under an alternating magnetic field. MNPs contained in nanofluid need to be transferred to tumor region before therapy can begin, and one of the most prominent methods is direct injection. Although different aspects of this area are covered in literature, the study of models which consider the combined effects of nanofluid transport and heat generation on the ablation of malignant cells still lacks enough attention. A complete computational model is developed in this paper to evaluate the survival rate of malignant cells for a proposed geometric model when intratumoral injection of MNPs is considered. The mathematical model incorporates the transport of nanofluid inside the bio-tissue, the heat generation of MNPs during ablation, the heat transfer of bio-tissue, and the cell death probability based on the Arrhenius model. The concentration distribution of nanofluid and the treatment temperature profile inside bio-tissue are obtained by considering the finite element method with the proposed boundary and initial conditions. Simulation results demonstrate that the death rate of malignant cells can be considerably improved when a proper critical power dissipation of MNPs is designed and enough diffusion duration is considered for therapy. With further developments, the model may be used for the planning of magnetic hyperthermia.     

抗血管生成治疗抑制实体肿瘤细胞生长的数值模拟:应用血管生成与肿瘤生长的耦合数学模型

为研究抗血管生成因子angiostatin和抗血管生成药物endostatin对肿瘤血管生成和肿瘤细胞的抑制作用,建立耦合肿瘤血管生长、肿瘤生长和血液灌注的数学模型．模拟结果显示抗血管生成因子angiostatin和抗血管生成药物endostatin可明显抑制血管生成和减少肿瘤细胞数量,从而起到改善肿瘤组织内部异常微环境的作用．模型可作为肿瘤抗血管生成治疗的一种理论研究．     

Numerical simulation of anomalous plasma transport in the presence of magnetic turbulence

The structure of plasma in the interplanetary space is briefly presented, and the problems related to the variability of solar activity are discussed. The features of magnetic turbulence in the solar wind are also described. Magnetic field fluctuations are one of the causes of enhanced transport both in laboratory and astrophysical plasmas. To a first approximation, the plasma particles follow the magnetic field lines, whose equations form a non-linear one and a half degrees of freedom system. Unless the fluctuation level is very low, numerical simulations are needed to study such a system. We review three-dimensional numerical simulations of field line transport in anisotropic magnetic turbulence. Several transport regimes are found: for low Kubo number, anomalous transport is obtained, featuring both subdiffusion, corresponding to trapping in cantori structures, and superdiffusion, corresponding to Levy flights in the stochastic layer. Increasing the Kubo number, and hence stochasticity, quasilinear, intermediate, and percolative regimes are found, in the order. An expression of the diffusion coefficient valid for generalized anisotropy is presented.