Edward P. Furlani

Analysis of particle transport in a magnetophoretic microsystem

An analytical analysis is presented of the transport and capture of magnetic micro/nanoparticles in a magnetophoretic microsystem that consists of an array of integrated soft-magnetic elements embedded beneath a microfluidic channel. The elements, which are polarized by a bias field, produce a nonuniform field distribution that gives rise to a force on magnetic particles within the microchannel. The equations governing particle motion are derived using analytical expressions for the dominant magnetic and fluidic forces. The magnetic force is obtained using an analytical expression for the field distribution in the microchannel combined with a linear magnetization model for the magnetic response of the particles. The theory takes into account particle size and material properties, the bias field, the dimensions of the microchannel, the fluid properties, and the flow velocity. The equations of motion are solved to study particle transport and capture. The analysis indicates that the particles exhibit an oscillatory motion as they traverse the microsystem, and that a high capture efficiency can be obtained in practice.

Magnetophoretic separation of blood cells at the microscale

We present a method for the direct and continuous separation of red and white blood cells from plasma at the microscale. The method is implemented in a microfluidic system with magnetic functionality. The fluidic structure within the microsystem consists of an inlet and a single microfluidic channel with multiple outlets. The magnetic functionality is provided by an array of integrated soft-magnetic elements that are embedded transverse and adjacent to the microchannel. The elements are magnetized using an external field, and once magnetized they produce a magnetic force on blood cells as they flow through the microchannel. In whole blood, white blood cells (WBCs) behave as diamagnetic microparticles, while red blood cells (RBCs) exhibit diamagnetic or paramagnetic behavior depending on the oxygenation of their hemoglobin. We study the motion of blood cells through the microchannel using a mathematical model that takes into account the magnetic, fluidic and gravitational forces on the cells. We use the model to study blood cell separation, and our analysis indicates that the microsystem is capable of separating WBC-rich plasma, deoxygenated RBC-rich plasma and cell-depleted plasma into respective outlets.

A two-dimensional analysis for the coupling of magnetic gears

A formula is presented for computing the coupling between magnetic gears. This formula, which is based on two-dimensional analytical analysis, is expressed as a finite sum of elementary functions and is well suited for parametric analysis. It is demonstrated via application to a practical device and verified using finite element analysis (FEA).

A model for predicting magnetic targeting of multifunctional particles in the microvasculature

A mathematical model is presented for predicting magnetic targeting of multifunctional carrier particles that are designed to deliver therapeutic agents to malignant tissue in vivo. These particles consist of a nonmagnetic core material that contains embedded magnetic nanoparticles and therapeutic agents such as photodynamic sensitizers. For in vivo therapy, the particles are injected into the vascular system upstream from malignant tissue, and captured at the tumor using an applied magnetic field. The applied field couples to the magnetic nanoparticles inside the carrier particle and produces a force that attracts the particle to the tumor. In noninvasive therapy, the applied field is produced by a permanent magnet positioned outside the body. In this paper, a mathematical model is developed for predicting noninvasive magnetic targeting of therapeutic carrier particles in the microvasculature. The model takes into account the dominant magnetic and fluidic forces on the particles and leads to an analytical expression for predicting their trajectory. An analytical expression is also derived for predicting the volume fraction of embedded magnetic nanoparticles required to ensure capture of the carrier particle at the tumor. The model enables rapid parametric analysis of magnetic targeting as a function of key variables including the size of the carrier particle, the properties and volume fraction of the embedded magnetic nanoparticles, the properties of the magnet, the microvessel, the hematocrit of the blood and its flow rate.

Subwavelength direct laser patterning of conductive gold nanostructures by simultaneous photopolymerization and photoreduction.

This article presents a new method for fabricating highly conductive gold nanostructures within a polymeric matrix with subwavelength resolution. The nanostructures are directly written in a gold precursor-doped photoresist using a femtosecond pulsed laser. The laser energy is absorbed by a two-photon dye, which induces simultaneous reduction of gold in the precursor and polymerization of the negative photoresist. This results in gold nanoparticle-doped polymeric lines that exhibit both plasmonic effects, due to the constituent gold nanoparticles, and relatively high conductivity (within an order of magnitude of the bulk metal), due to the high density of particles within these lines. Line widths from 150 to 1000 nm have been achieved with this method. Various optically functional structures have been prepared, and their structural and optical properties have been characterized. The influence of laser intensity and scan speed on feature size have been studied and found to be in agreement with predictions of a mathematical model of the process.

Formulas for the force and torque of axial couplings

Closed-form expressions are presented for computing the force and torque that is transmitted by synchronous axial couplings. These expressions enable rapid parametric studies of coupling performance relative to the selection of magnet material, dimensions, and spacings. They are also useful for testing three-dimensional numerically based field algorithms. The derived expressions are tested here using data taken from a ceramic coupling. >

A three-dimensional field solution for radially polarized cylinders

A three-dimensional field solution is presented for radially polarized permanent-magnet cylinders. The derived field formulae are evaluated in terms of finite sums of elementary functions. They are readily programmed and ideal for performing rapid parametric studies of the field distribution outside of cylinders made from rare earth materials such as NdFeB. The theory is demonstrated with some sample calculations that are verified by use of three-dimensional finite element analysis. >

The effect of static magnetic fields and tat peptides on cellular and nuclear uptake of magnetic nanoparticles.

Magnetic nanoparticles are widely used in bioapplications such as imaging (MRI), targeted delivery (drugs/genes) and cell transfection (magnetofection). Historically, the impermeable nature of both the plasma and nuclear membranes hinder potential. Researchers combat this by developing techniques to enhance cellular and nuclear uptake. Two current popular methods are using external magnetic fields to remotely control particle direction or functionalising the nanoparticles with a cell penetrating peptide (e.g. tat); both of which facilitate cell entry. This paper compares the success of both methods in terms of nanoparticle uptake, analysing the type of magnetic forces the particles experience, and determines gross cell response in terms of morphology and structure and changes at the gene level via microarray analysis. Results indicated that both methods enhanced uptake via a caveolin dependent manner, with tat peptide being the more efficient and achieving nuclear uptake. On comparison to control cells, many groups of gene changes were observed in response to the particles. Importantly, the magnetic field also caused many change in gene expression, regardless of the nanoparticles, and appeared to cause F-actin alignment in the cells. Results suggest that static fields should be modelled and analysed prior to application in culture as cells clearly respond appropriately. Furthermore, the use of cell penetrating peptides may prove more beneficial in terms of enhancing uptake and maintaining cell homeostasis than a magnetic field.

A three-dimensional field solution for permanent-magnet axial-field motors

A formula is presented for computing the field in axial-field permanent-magnet motors. The formula is based on a three-dimensional (3-D) analytical analysis and is expressed in terms of a finite sum of elementary functions. It is readily programmed and ideal for parametric studies of field strength. It is also well suited for parallel processing and could be developed into a motor model for real-time performance simulations. It is applied here to a practical motor geometry and verified by the use of 3-D finite element analysis (FEA).

Analytical analysis of magnetically coupled multipole cylinders

An analytical analysis is presented for the magnetic coupling between separated, radially-polarized multipole cylinders. These cylinders function as a magnetic gear and a formula is derived for computing the torque developed by such gears. The theory applies to rare-earth materials such as NdFeB, and is demonstrated via simulation of a practical device.