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The purpose of this paper is to present the basic ideas of magnetic nanoparticles' usage in the breast cancer treatment, which is called magnetic fluid hyperthermia. The proposed approach offers a relatively simple methodology of energy deposition, allowing an adequate temperature control at the target tissue, in this case a cancerous one. By means of a numerical method the authors aim to investigate two heating effects caused by varying magnetic fields, i.e. to compare the power density heating effects of eddy currents and magnetic nanoparticles.

In order to numerically investigate the combination of the overheating effect of magnetic nanoparticles and eddy currents, the Finite Element Method solver based on FEniCS project has been prepared. To include the magnetic fluid in the model it has been assumed that power losses in the magnetic nanoparticles are completely converted into heat, according to experimentally developed formula. That formula can be interpreted as the hysteresis losses with regard to the volume of magnetic fluid. Finally, the total power density has been calculated as the product of the sum of power density from eddy currents and hysteresis losses. That methodology has been applied to calculate the effectiveness of magnetic fluid hyperthermia with regard to the female breast phantom.

The paper presents the methodology which can be used in magnetic fluid hyperthermia therapy planning and Computer Aid Diagnosis (CAD). Furthermore, it is shown how to overcome one of the most serious engineering challenges connected with hyperthermia, i.e. achieving adequate temperature in deep tumors without overheating the body surface.

The obtained results connected with the assessment of eddy currents effect suggest that during hyperthermia treatment the configuration which consists of an exciting coil and human body, plays a curial role. Moreover, the authors believe that these results will help to predict the skin surface overheating that accompanies deep heating. The presented methodology can be used by engineers in the development of Computer Aid Diagnosis systems.

In a given patient's situation a number of choices must be made to determine the parameters of the hyperthermia treatment. These include the need of multiple‐point temperature measurements for accurate and thorough monitoring. Treatment planning will require accurate characterization of the applicator deposition pattern and the tissue parameters, as well as the numerical techniques to predict the resultant heating pattern. The presented paper shows how to overcome these problems from the numerical point of view at least.

Cancer is the foremost disease that causes death. The objective of hyperthermia in cancer therapy is to raise the temperature of cancerous tissue above a therapeutic value while maintaining the surrounding normal tissue at sublethal temperature values in cases where surgical intervention is dangerous or impossible. The malignant tissue is heated up to 42°C in the treatment. In this method, the unaffected tissues are aimed to have minimum damage, while the affected ones are destroyed. Therefore, it is very important for the optimization of the method to know the temperature profiles in both tissues. Accurately estimating the tissue temperatures has been a very important issue for tumor hyperthermia treatment planning. This paper, proposes to theoretically predict the temperature response of the biological tissues subject to external EM heating by using the space‐dependent blood perfusion term in Pennes bio‐heat equation.

The bio‐heat transfer equation is parabolic partial differential equation. Grid points including independent variables are initially formed in solution of partial differential equation by finite element method. In this study, one dimensional bio‐heat transfer equation is solved by flex‐PDE finite element method.

In this study, the bio‐heat transfer equation is solved for variable blood perfusion values and the temperature field resulting after a hyperthermia treatment is obtained. Homogeneous, non‐homogeneous tissue and constant, variable blood perfusion rates are considered in this study to display the temperature fields in the biological material exposed to externally induced electromagnetic irradiation.

Temperature‐dependent tissue thermophysical properties have been used and the Pennes equation is solved by FEM analysis. Variable blood perfusion and heat generation values have been used in calculations for healthy tissue and tissue with tumor.

The purpose of this study is to show that the methods of the numerical simulation can be a very effective tool for a proper choice of control parameters of artificial hyperthermia. An electromagnetic field induced by two external electrodes and a temperature field resulting from electrodes action in a 3D domain of biological tissue is considered. An important problem is the appropriate directing of heat in the region of tumor, so as to avoid damaging healthy cells surrounding the tumor. Recently, to concentrate the heat on the tumor, magnetic nanoparticles, which are introduced into the tumor, were used. The nanoparticles should be made of material that ensures appropriate magnetic properties and has a high biocompatibility with the biological tissue. External electric field causes the heat generation in the tissue domain.

The distribution of electric potential in the domain considered is described by the Laplace system of equations, while the temperature field is described by the Pennes’ system of equations. These problems are coupled by source function being the additional component in the Pennes’ equation and resulting from the electric field action. The boundary element method is applied to solve the coupled problem connected with the heating of biological tissues.

The aim of investigations is to determine an electric potential of external electrodes and the number of nanoparticles introduced to a tumor region to obtain the artificial hyperthermia state. The tests performed showed that the proposed tool to solve the inverse problem provides correct results.

In the paper the steady state bioheat transfer problem is considered, so the thermal damage is a function of the temperature only. Therefore, the solution can be considered as the maximum ablation zone of cancer. Additionally, the choice of appropriate parameters will be affected on the position and shape of the tumor and the electrodes.

In the paper the inverse problem has been solved using the evolutionary algorithm, gradient method and hybrid algorithm which is a combination of the two previous.

The purpose of this paper is to focus on applications related to the hyperthermia treatment of cancer, with heating imposed either by a laser in the near-infrared range or by radiofrequency waves. The particle filter algorithms are compared in terms of computational time and solution accuracy.

The authors extend the analyses performed in their previous works to compare three different algorithms of the particle filter, as applied to the hyperthermia treatment of cancer. The particle filters examined here are the sampling importance resampling (SIR) algorithm, the auxiliary sampling importance resampling (ASIR) algorithm and Liu & West’s algorithm.

Liu & West’s algorithm resulted in the largest computational times. On the other hand, this filter was shown to be capable of dealing with very large uncertainties. In fact, besides the uncertainties in the model parameters, Gaussian noises, similar to those used for the SIR and ASIR filters, were added to the evolution models for the application of Liu & West’s filter. For the three filters, the estimated temperatures were in excellent agreement with the exact ones.

This work may help medical doctors in the future to prescribe treatment protocols and also opens the possibility of devising control strategies for the hyperthermia treatment of cancer.

The natural solution to couple the uncertain results from numerical simulations with the measurements that contain uncertainties, aiming at the better prediction of the temperature field of the tissues inside the body, is to formulate the problem in terms of state estimation, as performed in this work.

The purpose of this paper is to continue studies previously reported with the primary focus of optimizing an inductor design. The potential benefits of hyperthermia for cancer therapy, particularly metastatic cancers of the prostate, may be realized by the use of targeted magnetic nanoparticles that are heated by alternating magnetic fields (AMFs).

To further explore the potential of this technology, a high‐throughput cell culture treatment system is needed. The AMF requirements for this research present challenges to the design and manufacture of an induction system because a high flux density field at high frequency must be created in a relatively large volume. Additional challenges are presented by the requirement that the inductor must maintain an operating temperature between 35 and 39°C with continuous duty operation for 1 h or longer. Results of simulation and design of two devices for culture samples and for in vitro tests of multiple samples in uniform field are described.

The inductor design chosen provides a uniform distribution of relatively high magnetic field strength while providing an optimal reduction in the voltage and power requirement. Through development of design and selection of magnetic concentrator, the exposure of the cell cultures to the heat generated by the inductor is minimized.

This method of generating uniform high AC magnetic fields in a large volume is beneficial for the study of hyperthermia in cells for a high throughput, necessary for cancer treatment research.

The purpose of this paper is to present the synthesis of magnetic fluid characteristics, like diameter of nanoparticles (NPs) and their concentration, in order to obtain a prescribed temperature rate. An evolution strategy algorithm is used in the optimization procedure, while three‐dimensional finite‐element (FE) modelling is used for magnetic field and thermal field analysis in transient conditions.

FE analysis has been used in order to compute the magnetic and thermal field in a suitable model of the tumor region. The power density due to NP has been accordingly derived.

The NP distribution, giving a prescribed thermal response, is synthesized.

The proposed method can be used to design a therapeutic treatment based on magnetic fluid hyperthermia.

The paper belongs to a streamline of innovative studies on computational hyperthermia.

The purpose of this paper is to investigate the behavior of a non-Newtonian nanofluid caused by peristaltic waves along an asymmetric channel. Additionally considered is the production of thermal radiation and activation energy.

The equations of momentum, mass and temperature of Sutterby nanofluids are obtained for long wavelength. By taking into account the velocity, temperature and concentration, the formulation is further finished.

Analyses of the physical variables influencing flow features are represented graphically. The present investigation shows that an enhancement in the temperature ratio parameter results in an increase in both the temperature and concentration. The investigation also shows that the dimensionless reaction rate significantly raises the kinetic energy of the reactant, which permits more particle collisions and as a result, raises the temperature field.

Due to their importance in the treatment of cancer, activation energy and thermal radiation as a route of heat transfer are crucial and exciting phenomena for researchers. So, the cancer cells are killed, and tumors are reduced in size with heat and making hyperthermia therapy a cutting-edge cancer treatment.

The purpose of this paper is to apply the Steady State Kalman Filter for temperature measurements of tissues via magnetic resonance thermometry. Instead of using classical direct inversion, a methodology is proposed that couples the magnetic resonance thermometry with the bioheat transfer problem and the local temperatures can be identified through the solution of a state estimation problem.

Heat transfer in the tissues is given by Pennes’ bioheat transfer model, while the Proton Resonance Frequency (PRF)-Shift technique is used for the magnetic resonance thermometry. The problem of measuring the transient temperature field of tissues is recast as a state estimation problem and is solved through the Steady-State Kalman filter. Noisy synthetic measurements are used for testing the proposed methodology.

The proposed approach is more accurate for recovering the local transient temperatures from the noisy PRF-Shift measurements than the direct data inversion. The methodology used here can be applied in real time due to the reduced computational cost. Idealized test cases are examined that include the actual geometry of a forearm.

The solution of the state estimation problem recovers the temperature variations in the region more accurately than the direct inversion. Besides that, the estimation of the temperature field in the region was possible with the solution of the state estimation problem via the Steady-State Kalman filter, but not with the direct inversion.

The recursive equations of the Steady-State Kalman filter can be calculated in computational times smaller than the supposed physical times, thus demonstrating that the present approach can be used for real-time applications, such as in control of the heating source in the hyperthermia treatment of cancer.

The original and novel contributions of the manuscript include: formulation of the PRF-Shift thermometry as a state estimation problem, which results in reduced uncertainties of the temperature variation as compared to the classical direct inversion; estimation of the actual temperature in the region with the solution of the state estimation problem, which is not possible with the direct inversion that is limited to the identification of the temperature variation; solution of the state estimation problem with the Steady-State Kalman filter, which allows for fast computations and real-time calculations.

Gives a bibliographical review of the finite element methods (FEMs) applied in biomedicine from the theoretical as well as practical points of view. The bibliography at the end of the paper contains 748 references to papers, conference proceedings and theses/dissertations dealing with the finite element analyses and simulations in biomedicine that were published between 1985 and 1999.

This paper aims to present the optimal design of an inductor used to heat a magnetic nanoparticle fluid injected in a cell culture inside a Petri dish.

The inductor design is driven by means of a multi-objective optimization algorithm that generalizes the migration-non-dominated sorting genetic algorithm (NSGA); it is called self-adapting migration-NSGA.

The optimized device is able to synthesize a uniform magnetic field in a nanoparticle fluid, substantially helping its heating capability. The ultimate scope is to assist the cancer therapy based on magnetic fluid hyperthermia (MFH).

The optimal design of an inductor for MFH applications has been carried out by applying an improved version of migration-based NSGA-II algorithm including automatic stop and a self-adapting concept. The modified optimization algorithm is suitable to find better optimal solutions with respect to a standard version of NSGA-II.