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We present a new algorithm for the numerical solution of problems of electromagnetic or acoustic scattering by large, convex obstacles. This algorithm combines the use of an ansatz for the unknown density in a boundary-integral formulation of the scattering problem with an extension of the ideas of the method of stationary phase. We include numerical results illustrating the high-order convergence of our algorithm as well as its asymptotically bounded computational cost as the frequency increases.

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In magnetic drug delivery, therapeutic magnetizable particles are typically injected into the blood stream and magnets are then used to concentrate them to disease locations. The behavior of such particles in-vivo is complex and is governed by blood convection, diffusion (in blood and in tissue), extravasation, and the applied magnetic fields. Using physical first-principles and a sophisticated vessel-membrane-tissue (VMT) numerical solver, we comprehensively analyze in detail the behavior of magnetic particles in blood vessels and surrounding tissue. For any blood vessel (of any size, depth, and blood velocity) and tissue properties, particle size and applied magnetic fields, we consider a Krogh tissue cylinder geometry and solve for the resulting spatial distribution of particles. We find that there are three prototypical behaviors (blood velocity dominated, magnetic force dominated, and boundary-layer formation) and that the type of behavior observed is uniquely determined by three non-dimensional numbers (the magneticRichardson number, mass Péclet number, and Renkin reduced diffusion coefficient). Plots and equations are provided to easily read out which behavior is found under which circumstances (Figures 5,6,7,and 8). We compare our results to previously published in-vitro and in-vivo magnetic drug delivery experiments. Not only do we find excellent agreement between our predictions and prior experimental observations, but we are also able to qualitatively and quantitatively explain behavior that was previously not understood. IntroductionMagnetic drug targeting refers to the attachment of therapeutics to magnetizable particles, and then applying magnetic fields to concentrate them to disease locations such as to solid tumors, regions of infection, or blood clots [4,[8][9][10][11][12][13][14]. Though in some cases the magnetizable particles can be introduced into the body outside the blood flow, e.g. as in magnetic treatment of the inner-ear where a small gel containing nano-particles is placed on the round window membrane [19,20], usually ferromagnetic particles are injected into a vein or artery [4][5][6][7]9,13,16,[21][22][23][24][25][26][27][28][29]. Particles so injected will circulate throughout the vasculature as the applied magnetic field is used to attempt confinement at target locations. Two main considerations arise from the in-vivo use of these particles. First, the particles must be small * Corresponding author, alek@umd.edu.Publisher's Disclaimer: This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final citable form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. NIH Public Access NIH-PA Author ManuscriptNIH-PA Author Manuscript NIH-PA...

We have recently introduced a method of variation of boundaries for the solution of diffraction problems. This method, which is based on a theorem of analyticity of the electromagnetic field with respect to variations of the interfaces, has been successfully applied in problems of diffraction of light by perfectly conducting gratings. In this paper we continue our investigation of diffraction problems. Using our previous results on analytic dependence with respect to the grating groove-depth, we present a new numerical algorithm which applies to dielectric gratings. We also incorporate Pade approximation in our numerics. This addition enlarges the domain of applicability of our methods, and it results in computer codes which can predict more accurately the response of diffraction gratings in the resonance region. In many cases, results are obtained which are several orders of magnitude more accurate than those given by other methods available at present, such as the integral or differential formalisms.We present a variety of numerical applications, including examples for several types of grating profiles and for wavelengths of light ranging from microwaves to ultraviolet, and we compare our results with experimental data. We also use Pade approximants to gain insight on the analytic structure and the spectrum of singularities of the fields as functions of the groove-depth. Finally, we discuss some connections between Pade approximation and another summation mechanism, enhanced convergence, which we introduced earlier. It is argued that, provided certain numerical difficulties can be overcome, the performance of our algorithms could be further improved by a combination of these summation methods.

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