Pinchas D. Einziger

Enhanced heat deposition using ultrasound contrast agent - modeling and experimental observations

Ultrasound contrast agents (UCA), created originally for visualization and diagnostic purposes, recently have been suggested as efficient enhancers of ultrasonic power deposition in tissue. The ultrasonic energy absorption by the contrast agents, considered as problematic in diagnostic imaging, might have beneficial impact in therapeutic applications such as targeted hyperthermia-based or ablation treatments. Introduction of gas microbubbles into the tissue to be treated can improve the effectiveness of current treatments by limiting the temperature rise to the treated site and minimising the damage to the surrounding healthy tissues. To this end, proper assessment of the governing parameters of energy absorption by ultrasonically induced stabilized bubbles is important for both diagnostic and therapeutic ultrasound applications. The current study was designed to predict theoretically and measure experimentally the dissipation and heating effects of encapsulated UCA in a well-controlled and calibrated environment. The ultrasonic effects of the microbubble concentration, transmitted intensity, and frequency on power dissipation and stability of the UCA have been studied. The maximal temperature elevation obtained during 300 s experiments was 21/spl deg/C, in a 10 ml volume target containing UCA, insonified by unfocused 3.2 MHz continuous wave (CW) at spatial average intensity of 1.1 W/cm/sup 2/ (182 kPa). The results also suggest that higher frequencies are more efficiently absorbed by commonly used UCA. In particular, for spatial average intensity of 1.1 W/cm/sup 2/ and concentration of 5/spl middot/10/sup 6/ microspheres/cm/sup 3/, no significant reduction of UCA absorption was noticed during the first 150 s for insonation at 3.2 MHz and the first 100 s for insonation at 1 MHz. In addition, when lower average intensity of 0.5 W/cm/sup 2/ (160 kPa) at 3.2 MHz was used, the UCA absorptivity sustained for almost 200 s. Thus, when properly activated, UCA may be suitable for localized hyperthermic therapies.

Evanescent waves and complex rays

Evanescent wave theory (EWT) is an extension of the geometrical theory of diffraction (GTD) to the tracking of high-frequency plane wave fields with complex phase. The tracking takes place along phase paths perpendicular to the local phase fronts. The determination of the generally complicated configuration of phase paths constitutes a difficulty in the implementation of EWT. The viability of an approximate scheme is examined whereby the phase paths emanating from the initial surface, on which the field is prescribed, are taken locally as hyperbolas; these are known to represent exact global solutions of a particular canonical evanescent wave problem. Numerical comparisons to be presented elsewhere reveal, however, that the local hyperbolic phase path matching may generally be inadequate even for weakly evanescent fields, although this procedure is effective for certain types of initial conditions. To overcome this difficulty, the solution is obtained from an exact formulation involving field integration over the intital surface and subsequent asymptotic evaluation by the saddle point method. Since the saddle points are complex, the latter procedure is equivalent to an analysis in terms of complex rays, from which one may derive the phase paths of EWT. Therefore complex rays should be used as an algorithm for solving the phase path equations. The rigorous analysis also shows that complex ray theory, or EWT, cannot account for strongly evanescent fields, and that there may exist relevant ray contributions from deep within the complex space that cannot be found by the real-space tracking of EWT.

Complex rays for radiation from discretized aperture distributions

Many electromagnetic propagation problems require tracking of fields radiated by large actual or induced aperture distributions through complicated environments before reaching the observer. For a systematic approach to this problem area, it is desirable to represent the aperture field in terms of basis functions which are physically informative and well adapted to traversing the propagation path. At high frequencies, Ganssian beam-type basis functions meet these requirements. After referring to a rigorous aperture discretization scheme, various quasi-Gaussian basis field profiles are examined, with a special view toward expressing their radiation properties in terms of complex rays; complex ray tracing is promising for field tracking in complicated surroundings. By comparing reference solutions from numerical integration of radiation integrals with complex ray asymptotics, it is concluded that the true Gaussian has the most favorable attributes for matching aperture discretization, propagation requirements, and complex ray tracing. Thus, the analysis here may point the way toward systematic treatment of the above-noted class of propagation problems.

Interaction of array of finite electrodes with layered biological tissue: effect of electrode size and configuration

A hybrid scheme, combining image series and moment method has been utilized for the calculation of the intramuscular three-dimensional (3-D) current density (CD) distribution and potential field transcutaneously excited by an electrode array. The model permits one to study the effect of tissue electrical properties and electrode placement on the CD distribution. The isometric recruitment curve (IRC) of the muscle was used for parameter estimation and model verification, by comparison with experimentally obtained IRCs of functional electrical stimulation (FES)-activated quadriceps muscle of paraplegic subjects. Sensitivity of the calculated IRC to parameters such as tissue conductivity, electrode size, and configuration was verified. The resulting model demonstrated characteristic features that were similar to those of experimentally obtained data. The model IRCs were insensitive to the electrode size; however, the inclusion of the bone-fascia layer significantly increased the intramuscular CD and, consequently, increased the IRC slope. Of the different configurations studied, a four-electrode array proved advantageous because, in this case, the CD between the electrodes was more evenly distributed, providing better resistance to fatigue. However, due to the steeper linear portion of the IRC, this configuration suffered from a somewhat reduced controllability of the muscle.

Rigorous image-series expansions of quasi-static Green's functions for regions with planar stratification

A novel image-series expansion scheme for quasi-static Greens function in n+1 layered media is obtained by expanding the frequency-dependent Hertz potential in finite expansions and remainder terms. The expansions utilize a unique recursive representation for Greens function, which is a generic characteristic of the stratification, and are explicitly constructed for n/spl les/3. While results for 0/spl les/n/spl les/2 are given for reference only, the expansion scheme for a double-slab configuration, n=3, is quite general and outlines the procedure for n>3, without any increase in the complexity. The expansion-remainder terms can be made negligibly small for sufficiently large summation indices in the quasi-static limit, leading to rigorous image-series expansion. The image-series convergence is accelerated by including a collective image term, representing a closed-form asymptotic evaluation of the series-remainder integral. Thus, the proposed computational procedure can be used as a simple tool for producing analytical data for testing numerical subroutines applied to direct problems such as electrical simulation of muscles in the biomedical field and inverse problems, such as electromagnetic imaging.

Rigorous Green's function formulation for transmembrane potential induced along a 3-D infinite cylindrical cell

The quasi-static electromagnetic field interaction with three-dimensional infinite-cylindrical cell is investigated for both intracellular (IPS) and extracellular (EPS) current point-source excitation. The induced transmembrane potential (TMP), expressed conventionally via Greens function, may alternatively be expanded into a faster-converging representation using a complex contour integration, consisting of an infinite-discrete set of exponentially decaying oscillating modes (corresponding to complex eigenvalues) and a continuous source-mode convolution integral. The dominant contributions for both the IPS and EPS problems are obtained in simple closed-form expressions, including well documented special mathematical functions. In the IPS case, the dominant modal contribution (of order zero)-an exact solution of the well-known cable equation-is explicitly and analytically corrected by the imaginary part of its eigenvalue and the source-mode convolution contribution. However, the TMP along a fiber was shown to decay at infinity algebraically and not exponentially, as predicted by the classic cable equation solution. In the EPS case, the dominant contribution is expressed as a source-mode convolution integral. However, for a long EPS distance (e.g., >10 cable length constant) the order-one-modes involved in the convolution is not a solution of the cable equation. Only for shorter EPS distance should the cable equation solution (i.e., the order zero dominant mode) be included in addition to the modes of order one. For on-membrane EPS location, additional modes should be included as well. In view of our EPS result, we suggest that the cable equation modeling existing in the literature and related to functional electrical stimulation for EPS problems, should be critically reviewed and corrected.

Current distribution in skeletal muscle activated by functional electrical stimulation: image-series formulation and isometric recruitment curve.

AbstractThe present work develops an analytical model that allows one to estimate the current distribution within the whole muscle and the resulting isometric recruitment curve (IRC). The quasistatic current distribution, expressed as an image series, i.e., a collection of properly weighted and shifted point-source responses, outlines an extension for more than three layers of the classical image theory in conductive plane-stratified media. Evaluation of the current distribution via the image series expansions requires substantially less computational time than the standard integral representation. The expansions use a unique recursive representation for Greens function, that is a generic characteristic of the stratification. This approach permits one to verify which of the tissue electrical properties are responsible for the current density distribution within the muscle, and how significant their combinations are. In addition, the model permits one to study the effect of different electrode placement on the shape and the magnitude of the potential distribution. A simple IRC model was used for parameter estimation and model verification by comparison with experimentally obtained isometric recruitment curves. Sensitivity of the model to different parameters such as conductivity of the tissues and activation threshold was verified. The resulting model demonstrated characteristic features that were similar to those of experimentally obtained data. The model also quantitatively confirmed the differences existing between surface (transcutaneous) and implanted (percutaneous) electrode stimulation.

A method of moments analysis of electromagnetic coupling through slots using a Gaussian beam expansion

A moment solution is presented for the problem of transverse electric (to the slot axis) electromagnetic coupling through a slot in infinitesimally thin, perfectly conducting screen separating two identical or contrasting half-space regions. The moment solution uses sets of properly shifted and modulated Gaussian elementary beams to expand the unknown equivalent magnetic current and a simple point-matching procedure for testing. The Gaussian expansion offers a numerical advantage in subsequent field calculations. Instead of integrating over surface currents when computing the fields, the proposed expansion allows the evaluation of the fields by summations of analytic terms exploiting the simple and well-understood propagation features of Gaussian beams. Sample computations are given and compared with a standard pulse-pulse Galerkin solution. >

Generalized transmission-line model for estimation of cellular handset power absorption in biological tissues

Evaluation of cellular handset power absorption in biological tissues has recently received due public attention. Generally, the solution of even simple cellular phone-human head configurations, involves massive and time consuming excitation of numerical algorithms. Furthermore, an explicit dependence of numerical solution on the physical parameters as well as on the configuration geometry is usually difficult to achieve. Herein, we focus on a generalized one-dimensional transmission-line model, which is capable of establishing tight bounds and estimates on the actual power absorption and radiation for many realistic configurations. The solution is given by explicit closed-form expressions, which depend continuously on the physical and geometrical parameters of the problem and, thus, can be readily physically interpreted. The potential promise of our simplified model is numerically verified via alternative finite-difference time-domain and moment method data for cellular handsets closely coupled to human head.

The Impact of Spectral and Spatial Exciton Distributions on Optical Emission From Thin-Film Weak-Microcavity Organic Light-Emitting Diodes

We present an analytical model for the optical emission produced by sources located in a thin-film weak-microcavity formation and study the effects of the ensemble spectral and spatial distribution on the device emission properties. However derived for a general stratified media configuration, the formulation results are highly applicable for the study of nanometric organic light-emitting devices. Rigorously developed into closed-form analytical expressions using the devices thin-film weak-microcavity characteristics, they enable clear observation of the underlying physical processes that determine the emission properties of the device, as well as the impact of the exciton ensemble spectral and spatial distributions on these properties. For the sake of simplicity and clarity, we focus on a 2-D canonical configuration excited by impulsive (line) sources. Our results show that the spectral distribution of the ensemble diminishes interference effects originated in the weak microcavity formed between the substrate/air and cathode/active layer interfaces, while the spatial distribution can only impact the slow-varying component of the emission pattern, which is the consequence of the source-image interference near the highly reflecting cathode. For a typical device, the quasi-Lambertian emission pattern reported experimentally is reproduced. It should be pointed out that the incorporation of both rigorous electromagnetic analysis and the source spectral and spatial broadening effects is addressed in our report, to the best of our knowledge, for the first time. This results in a precise model capable of repeating and interpreting experimental and simulated data.