Numerical optimization of 3-D SAR distributions in cylindricalmodels for electromagnetic hyperthermia

Numerically optimized SAR (specific absorption rate) distributions in a source free 3-D multilayered concentric cylindrical (MCC) model are presented. The fields were expanded in the modes of the MCC. Cost functions which specify mathematically the relative weight assigned to differences between an SAR distribution and a desired SAR distribution were defined. The coefficients of the modes, which minimize the cost function, were obtained using gradient search optimization methods. The optimized SAR distributions shown were computed using three different cost functions and two different radial locations for the center of the region where the desired SAR is largest. A five-layered model, including the outer water layer for cooling and improved matching with the source, was used. The frequency was 70 MHz. The current and charge distributions computed on a perfectly conducting cylindrical surface just outside the model are also shown. The surface current and charge distributions depend strongly on the relative importance of the cost for acute heat and systemic heat. A technique is developed for generating a new set of basis functions for reducing the number of unknowns to be optimized. We suggest that the approach shown could be useful in designing hyperthermia applicators.     

Numerical simulation of magnetic induction heating of tumors with ferromagnetic seed implants

Calculations based on the bioheat transfer equation have been carried out to determine the temperature distributions to be expected from the use of inductively heated ferromagnetic implants to heat deep-seated tumors. Two types of ferromagnetic implants are considered: constant power seeds, for example, those constructed from Type 430 stainless steel; and constant temperature seeds which pass through a Curie transition to the nonmagnetic state at a specified temperature. The temperature distributions are studied as a function of the size of the implant array, its geometrical relationship to the tumor, the density of implants within the array, and the blood perfusion characteristics of the tumor and its surrounding normal tissue. Two tumor models are considered: a uniformly perfused model which is indistinguishable from the surrounding normal tissue, and an annular perfusion model with a necrotic core surrounded by intermediately and highly perfused shells. Temperature distributions are considered acceptable if the minimum temperature in the tumor is greater than 42°C and the maximum temperature does not exceed a maximum allowable value (either 48 or 60°C). The results of over 200 combinations of the above parameters are presented in a compact format. General conclusions drawn are that the tumor should lie entirely within the implanted array if the tumor periphery is to be heated adequately, and that the constant temperature seeds, which are self-regulating in temperature, give better tumor temperature distributions.     

Nonlinear thermal model of a heterojunction-based light-emitting diode

A mathematical nonlinear thermal model of a heterojunction-based light-emitting diode (LED) is considered; the model makes it possible to estimate the nonuniformity of the current and temperature distributions in the active region of the heterostructure with the LED efficiency and the temperature dependence of the thermal-conductivity coefficient in the structure taken into account. A numerical-analytical iteration method is used to solve a set of equations that includes solving a nonlinear time-independent equation of thermal conductivity with the density of electrical power converted to heat dependent on the LED efficiency and an equation of electrothermal feedback, under conditions of a constant value for the average current density over the active region of the structure. The results of theoretical and experimental studies into the dependence of the p-n junction-to-case thermal resistance on the forward current are represented for high-power light-emitting diodes.     

Estimation of blood perfusion using phase shift in temperatureresponse to sinusoidal heating at the skin surface

A closed form analytical solution of the Pennes' bio-heat equation was obtained for temperature distributions in the skin tissue subject to the sinusoidal heat flux. Phase shifts in the surface temperature response were revealed to be related to local blood perfusion rate and heating frequency. The influence of the thermal contact resistance on the perfusion estimation was investigated. It has been proved that this influence is relatively small because of the phase shift based estimation and can be effectively eliminated by application of highly conductive grease. This analysis provides the theoretical foundation for a new noninvasive modality of blood perfusion estimation based on the surface temperature measurement which can have significant applications in future clinical practices.     

Electromagnetic and thermal models of a water-cooled dipoleradiating in a biological tissue

An insulated, water-cooled dipole, radiating in a biological tissue, is analyzed with a theoretical electromagnetic and thermal model. The SAR and temperature distributions are calculated taking into account the effect of the water flowing inside the applicator. The steady-state temperatures in a dissipative medium, interacting with the dipole, are evaluated for several thicknesses of the external casing, water temperatures and blood perfusions. A correct design of the external casing thickness and a proper choice of the temperature and flow velocity of water allows to control the wall temperature of the applicator within physiological limits. The influence of the blood perfusion on the temperature distribution is investigated.     

Inverse techniques in hyperthermia: a sensitivity study

Numerical modeling methods and hyperthermia treatment temperature measurements have been used together to reconstruct steady-state tumor temperature distributions. However, model errors will exist which may in turn produce errors in the reconstructed temperature distributions. A series of computer experiments was conducted to study the sensitivity of reconstructed two-dimensional temperature distributions to perfusion distribution modeling errors. Temperature distributions were simulated using a finite element approximation of Pennes' bioheat transfer equation. Relevant variables such as tumor shape, perfusion distribution, and power deposition were modeled. An optimization method and the temperatures “measured” from the simulated temperature distributions were used to reconstruct the tumor temperature distribution. Using this procedure, the sensitivity of the reconstructed tumor temperature distribution to model-related errors, such as the perfusion function, was studied. It was found that: 1) if the problem is conduction dominated, large errors in the perfusion distribution produce only small errors in the reconstructed temperature distribution (maximum error <1.0°C), and 2) when the actual perfusion distribution contains a small random variation (±15%) which is neglected by the model, the reconstructed temperature distribution mill be in good agreement with the actual temperature distribution (maximum error ⩽0.3°     

Nonlinear gain suppression in semiconductor lasers due to carrier heating

A simple model is presented for carrier heating in semiconductor lasers from which the temperature dynamics of the electron and hole distributions can be calculated. Analytical expressions for two new contributions to the nonlinear gain coefficient, in are derived, which reflect carrier heating due to stimulated emission and free carrier absorption. In typical cases, carrier heating and spectral holeburning are found to give comparable contributions to nonlinear gain suppression. The results are in good agreement with recent measurements on InGaAsP laser diodes.<>     

基于遗传算法的热疗温度场重构参数辨识方法

本文主要研究在肿瘤热疗中利用测量有限个温度点作参数辨识重构温度场的问题.为求取在生物传热中起主要作用的血液灌注率的优化参数估计,本文首次提出用遗传算法构造血液灌注率的参数辨识过程;这一方法在离线的仿真中得到了最优的高精度参数辨识,并且是模型自动匹配的.遗传算法在生物传热控制上所作的非线性参数辨识,也为控制中此类问题的研究提供了方法性依据.     

Nonlinear analysis of microwave superconductor devices usingfull-wave electromagnetic model

This paper presents a full electromagnetic wave analysis for modeling the nonlinearity in high temperature superconductor (HTS) microwave and millimeter-wave devices. The HTS nonlinear model is based on the Ginzburg-Landau theory. The electromagnetic fields associated with the currents on the superconducting structure are obtained using a three-dimensional full wave solution of Maxwell's equations. A three-dimensional finite-difference time-domain algorithm simultaneously solves the resulting equations. The entire solution is performed in time domain, which is a must for this type of nonlinearity analysis. The macroscopic parameters of the HTS, the super fluid penetration depth and the normal fluid conductivity, are calculated as functions of the applied magnetic field. The nonlinear propagation characteristics for HTS transmission line, including the effective dielectric constant and the attenuation constant, are calculated, As the power on the transmission line increases, the phase velocity decreases and the line losses increase. The nonlinearity effects on the current distributions inside the HTS, the electromagnetic field distributions, and the frequency spectrum are also analyzed     

A fast and simple algorithm for the calculation of convective heattransfer by large vessels in three-dimensional inhomogeneoustissues

A fast and simple algorithm has been presented for the calculation of time-dependent temperature distributions in inhomogeneous vascularized tissue. Three-dimensional anatomical data of tissues and vessel structures are decomposed into elementary cubic nodes by a special digitizing routine with vessels represented by connected strings of vessel nodes. Vessel cross sections may be irregular shaped and/or tapered. Conductive and convective heat transfer was calculated through use of the heat balance technique on each cubic node resulting in an explicit finite difference computational scheme. Employing a three time level scheme, the Fourier stability criterion is circumvented allowing arbitrary time steps to be defined in the algorithm. Time steps as large as 100 times the Fourier restricted one still result in stable and convergent calculations of the stationary temperature distribution. Vessels with different flows and diameters are incorporated by performing a vessel specific second discretization step in time. Using the new algorithm as a mathematical tool the thermal equilibration length of vessel segments have been established under a broad range of geometrical and flow conditions. Validation followed from comparing transient and stationary temperature distributions derived by the proposed algorithm to those from an accurate cylindrical numerical model. Predicted values for the thermal equilibration lengths are compared to an analytical expression and phantom experiments. The algorithm is incorporated in a thermal model being the main part of our hyperthermia treatment planning system.     

MINIMOS 3: A MOSFET simulator that includes energy balance

We present a model for hot carrier transport which is implemented in the device simulator MINIMOS 3. A brief resume of the model is given. We present various results which were calculated with this new model. We show that the I-V characteristics of a MOSFET can be calculated from Leff= 10 µm down to Leff= 0.9 µm with one parameter set. Modifications of carrier and current distributions are presented that show how hot carrier effects tend to smooth these distributions. Implications are discussed how a self-consistent carrier temperature can be used to model impact ionization and oxide injection.     

Finite-Element Analysis of Ex Vivo and In Vivo Hepatic Cryoablation

Cryoablation is a widely used method for the treatment of nonresectable primary and metastatic liver tumors. A model that can accurately predict the size of a cryolesion may allow more effective treatment of tumor, while sparing normal liver tissue. We generated a computer model of tissue cryoablation using the finite-element method (FEM). In our model, we considered the heat transfer mechanism inside the cryoprobe and also cryoprobe surfaces so our model could incorporate the effect of heat transfer along the cryoprobe from the environment at room temperature. The modeling of the phase shift from liquid to solid was a key factor in the accurate development of this model. The model was verified initially in an ex vivo liver model. Temperature history at three locations around one cryoprobe and between two cryoprobes was measured. The comparison between the ex vivo result and the FEM modeling result at each location showed a good match, where the maximum difference was within the error range acquired in the experiment (< 5 degC). The FEM model prediction of the lesion size was within 0.7 mm of experimental results. We then validated our FEM in an in vivo experimental porcine model. We considered blood perfusion in conjunction with blood viscosity depending on temperature. The in vivo iceball size was smaller than the ex vivo iceball size due to blood perfusion as predicted in our model. The FEM results predicted this size within 0.1-mm error. The FEM model we report can accurately predict the extent of cryoablation in the liver.     

Finite-element analysis of ex vivo and in vivo hepatic cryoablation.

Cryoablation is a widely used method for the treatment of nonresectable primary and metastatic liver tumors. A model that can accurately predict the size of a cryolesion may allow more effective treatment of tumor, while sparing normal liver tissue. We generated a computer model of tissue cryoablation using the finite-element method (FEM). In our model, we considered the heat transfer mechanism inside the cryoprobe and also cryoprobe surfaces so our model could incorporate the effect of heat transfer along the cryoprobe from the environment at room temperature. The modeling of the phase shift from liquid to solid was a key factor in the accurate development of this model. The model was verified initially in an ex vivo liver model. Temperature history at three locations around one cryoprobe and between two cryoprobes was measured. The comparison between the ex vivo result and the FEM modeling result at each location showed a good match, where the maximum difference was within the error range acquired in the experiment (< 5 degrees C). The FEM model prediction of the lesion size was within 0.7 mm of experimental results. We then validated our FEM in an in vivo experimental porcine model. We considered blood perfusion in conjunction with blood viscosity depending on temperature. The in vivo iceball size was smaller than the ex vivo iceball size due to blood perfusion as predicted in our model. The FEM results predicted this size within 0.1-mm error. The FEM model we report can accurately predict the extent of cryoablation in the liver.     

Control of the cryosurgical process in nonideal materials

A study of a controlled cryosurgical process is presented. This study is based on the energy equations describing the probe response and the phase change occurring in the medium. First-order nonlinear differential equations (state equations) are obtained by applying the integral-solution method. In order to obtain maximal cell destruction, it is desired to control a specific cooling rate at the solid-liquid interface. This cooling rate defines the desired trajectories of the state variables through the state equations. In order to satisfy the cooling rate condition on the freezing front, a closed-loop is designed to control the probe temperature program. A simple analysis of the system stability employed linearization at several points along the desired trajectories. Ranges of stability were obtained for a system containing a proportional-integral controller. It was demonstrated that these stability ranges depend mainly on the selected sampling time of the discrete control loop and that the phase-change process does not significantly affect the stability results. A complete study of the nonlinear equations was performed by a computer simulation program which enables the selection of the final values of the controller parameters, in order to minimize the error and to ensure stability. In addition, the simulation program gives information about the effects of the A/D and D/A converters accuracy on the performance of the control loop. An A/D converter accuracy of 12 bits was found necessary in order to reduce the oscillations in probe temperature to acceptable values. The simulation also yields a complete calculated temperature field in the tissue during the controlled process. From these simulated results it can be seen that oscillations of +/- 0.5 degrees C in the desired probe temperature do not significantly affect the desired cooling rate at the freezing front. An initial overshoot of 1.5 degrees C in the desired probe temperature was obtained both experimentally and theoretically from the simulation. When this initial overshoot occurs at the beginning of the freezing process, it causes an error in freezing front velocity and consequently in ice-front position. From the numerical simulation, it can be deduced that the cooling rate obtained at the front deviates from the desired value by approximately 1%. The probe-temperature error increases at two instants: a) during the super-cooling effect and the subsequent sudden crystallization, and b) when the probe temperature is below -80 degrees C and unstable boiling of the cooling medium causes oscillations.     

Optimal steady-state temperature distribution for a phased arrayhyperthermia system

A method is presented for the evaluation of optimal amplitude and phase excitations for the radiating elements of a phased array hyperthermia system, in order to achieve desired steady-state temperature distributions inside and outside of malignant tissues. Use is made of a detailed electromagnetic and thermal model of the heated tissue in order to predict the steady-state temperature at any point in tissue. Optimal excitations are obtained by minimizing the squared error between desired and model predicted temperatures inside the tumor volume, subject to the constraint that temperatures do not exceed an upper bound outside the tumor. The penalty function technique is used to solve the constrained optimization problem. Sequential unconstrained minima are obtained by a modified Newton method. Numerical results for a four element phased array hyperthermia system are presented     

Output Power PDF of a Saturated Semiconductor Optical Amplifier: Second-Order Noise Contributions by Path Integral Method

We have developed a second-order small-signal model for describing the nonlinear redistribution of noise in a saturated semiconductor optical amplifier. In this paper, the details of the model are presented. A numerical example is used to compare the model to statistical simulations. We show that the proper inclusion of second-order noise terms is required for describing the change in the skewness (third-order moment) of the noise distributions. The calculated probability density functions are described far out in the tails and can hence describe signals with very low bit error rate (BER). The work is relevant for describing the noise distribution and BER in, for example, optical regeneration.     

Effect of second-order temperature jump in Metal-Oxide-Semiconductor Field Effect Transistor with Dual-Phase-Lag model

The present numerical investigation is concerned with the role of second-order temperature jump in a horizontal planar micro-channel heat transfer. We solve numerically Dual-Phase-Lag model in a two dimensional configuration coupled with a new jump boundary condition. The nanodevice of model consists of Metal-Oxide-Semiconductor Field Effect Transistor with either uniform or non-uniform heat generation. A new temperature jump boundary condition of first and second order is used especially in the oxide–semiconductor interface. The finite element method is used to bring forth the results for a 10 nm channel length of the transistor. Thermal properties of transistor device have been investigated for different orders of the temperature jump boundary condition. It has already been deduced that the increasing orders of temperature jump boundary condition lead to an increase of phonon-wall collisions. This new condition can lead to a significant increase in the heat flux and the calculated lattice temperature.     

一种新的植被热红外辐射模型

以植被的能量平衡方程为基础,根据植被内的湍流交换模式及辐射能的传输过程,考虑了风速、气温和水汽压廓线等影响,建立了一个适合于林冠的3层植被热红外辐射模型.用了新的计算方法,大大地提高了模型收敛速度.实验数据检验结果表明:所建的模型能正确地模拟植被各层温度随不同气象条件、不同植被结构等参数的变化.     

Investigation of the thermal performance of micro-whisker structured silicon heat spreaders for power devices

The driving forces of developments in power electronics are the continuing miniaturization and enhancement of power densities. New packaging concepts are required allowing the dissipation of a power loss density of up to several hundred W/cm² at operation temperatures as low as possible. A promising attempt to decrease the thermal resistance to the ambient is the development of silicon substrates structured with microwhiskers perpendicular to its surface. An industrial application of this new heat spreader technology in power electronic modules makes necessary the specification of the substrate properties. In this work, a new method for determination of thermal qualities based on laser heating of the heat spreader, surface temperature measurement by thermovision, and dynamic reverse modeling is described. For numerical determination of the thermal characteristics, the measured data are evaluated with the help of a thermal model of the heat spreaders under various boundary conditions. The respective temperature distributions are calculated with a new simulation tool using an alternating-direction implicit algorithm (ADI-method). Results obtained from heat spreaders with microwhisker treatment are compared with those from reference samples with a polished surface. Based on these results a view on future applications for power electronics assemblies are derived.