Analytical Solution for the Prediction of Temperature Distributions During Radio-Frequency Ablation of Cardiac Tissue

2003 ◽  
Author(s):  
Ryan T. Roper ◽  
Matthew R. Jones
Keyword(s):  
Analytical Solution ◽  
Radio Frequency ◽  
Numerical Solutions ◽  
Two Dimensions ◽  
Three Dimensions ◽  
Tissue Temperature ◽  
Bench Mark ◽  
Bioheat Equation ◽  
Surface Integral ◽  
Temperature Distributions

One of the most effective methods of treatment for cardiac arrhythmias is radio-frequency (RF) ablation. Many studies have shown that the tissue temperature distribution is the key factor influencing lesion shape and size, and that accurate prediction of this distribution is essential to the further improvement of the procedure. Temperature distributions can be obtained by solving the bioheat equation, which has been done in several studies using numerical techniques. This paper describes the development of an analytical solution that can be used as a bench mark for subsequent numerical solutions. Using integral transforms, the bioheat equation is reduced to an ordinary differential equation with time as the independent variable. The solution has the form of a surface integral within another surface integral. An integration routine that extends the trapezoidal method of integration in two dimensions to an analogous method in three dimensions has been developed in order to evaluate the analytical solution. A C program was written to implement this method, and the program was validated using a surface integral with a known analytical solution. The program was then used to generate temperature profiles at various time values and for different convection coefficients.

Benchmark Solution for the Prediction of Temperature Distributions During Radiofrequency Ablation of Cardiac Tissue

2004 ◽  
Vol 126 (4) ◽  
pp. 519-522 ◽  
Author(s):  
Ryan T. Roper and ◽  
Matthew R. Jones
Keyword(s):  
Cardiac Tissue ◽  
Numerical Solutions ◽  
Integral Transforms ◽  
Tissue Temperature ◽  
Temperature Profiles ◽  
Bioheat Equation ◽  
Temperature Distributions ◽  
Axial Temperature ◽  
Program Temperature ◽  
Benchmark Solution

Several studies on radiofrequency (RF) ablation are aimed at accurately predicting tissue temperature distributions by numerical solution of the bioheat equation. This paper describes the development of a solution that can serve as a benchmark for subsequent numerical solutions. The solution was obtained using integral transforms and evaluated using a C program. Temperature profiles were generated at various times and for different convection coefficients. In addition, a numerical model was developed using the same assumptions made in obtaining the benchmark solution. Comparison of surface and axial temperature profiles shows that the two solutions match very closely, cross validating the numerical methods used in evaluating both solutions.

MULTIDOMAIN PSEUDOSPECTRAL TIME-DOMAIN (PSTD) METHOD FOR ACOUSTIC WAVES IN LOSSY MEDIA

2004 ◽  
Vol 12 (03) ◽  
pp. 277-299 ◽  
Author(s):  
YAN QING ZENG ◽  
QING HUO LIU ◽  
GANG ZHAO
Keyword(s):  
Acoustic Wave ◽  
Time Domain ◽  
Acoustic Waves ◽  
Numerical Solutions ◽  
Two Dimensions ◽  
Three Dimensions ◽  
Curvilinear Coordinates ◽  
Computational Domain ◽  
Complex Objects ◽  
Lossy Media

A multidomain pseudospectral time-domain (PSTD) method is developed for acoustic wave equations in lossy media. The method is based on the spectral derivative operator approximated by Chebyshev Lagrange polynomials. In this multidomain scheme, the computational domain is decomposed into a set of subdomains conformal to the problem geometry. Each curved subdomain is then mapped onto a cube in the curvilinear coordinates so that a tensor-product Chebyshev grid can be utilized without the staircasing error. An unsplit-field, well-posed PML is developed as the absorbing boundary condition. The algorithm is validated by analytical solutions. The numerical solutions show that this algorithm is efficient for simulating acoustic wave phenomena in the presence of complex objects in inhomogeneous media. To our knowledge, the multidomain PSTD method for acoustics is a new development in three dimensions, although in two dimensions the method can be made equivalent to the two-dimensional method in electromagnetics.

scholarly journals Analytical solution of the bioheat equation for thermal response induced by any electrode array in anisotropic tissues with arbitrary shapes containing multiple-tumor nodules

2019 ◽  
Vol 65 (3) ◽  
pp. 284
Author(s):  
E. J. Roca Oria ◽  
L. E. Bergues Cabrales ◽  
And J. Bory Reyes
Keyword(s):  
Analytical Solution ◽  
Initial Temperature ◽  
Electrode Array ◽  
Thermal Response ◽  
Electrochemical Treatment ◽  
Bioheat Transfer ◽  
Heat Sources ◽  
Bioheat Equation ◽  
Multiple Tumor ◽  
Temperature Distributions

The Pennes bioheat transfer equation is the most used model to calculate the temperature induced in a tumor when physical therapies like electrochemical treatment, electrochemotherapy and/or radiofrequency are applied. In this work, a modification of the Pennes bioheat equation to study the temperature distribution induced by any electrode array in an anisotropic tissue containing several nodules (primary or metastatic) with arbitrary shape is proposed. For this, the Green functions approach is generalized to include boundaries among two or more media. The analytical solution we obtain in a very compact way, under quite general suppositions, allows calculating the temperature distributions in the tumor volumes and their surfaces, in terms of heat sources, initial temperature and calorific sources at the boundary of tumors.

scholarly journals Thermal Detection of Embedded Tumors Using Infrared Imaging

2004 ◽  
Author(s):  
Manu Mital ◽  
E. P. Scott
Keyword(s):  
Breast Cancer ◽  
United States ◽  
Genetic Algorithm ◽  
Temperature Distribution ◽  
Infrared Imaging ◽  
Estimation Method ◽  
The United States ◽  
Tissue Temperature ◽  
Bioheat Equation ◽  
Temperature Distributions

Breast cancer is the most common cancer among women. Statistics released by American Cancer Society (1999) show that every 1 in every 8 women in the United States is likely to get breast cancer during her lifetime. Thermography, also known as thermal or infrared imaging, is a procedure to determine if an abnormality is present in the breast tissue temperature distribution, which may indicate the presence of an embedded tumor. In the year 1982, United States Food and Drug Administration (FDA) approved thermography as an adjunct method of detecting breast cancer, which could be combined with other established techniques like mammography. Although thermography is currently used to indicate the presence of an abnormality, there are no standard protocols to interpret the abnormal thermal images and determine the size and location of an embedded tumor. This research explores the relationship between the physical characteristics of an embedded tumor and the resulting temperature distributions on the skin surface. Experiments were conducted using a resistance heater that was embedded in agar in order to simulate the heat produced by a tumor in the biological tissue. The resulting temperature distribution on the surface was imaged using an infrared camera. In order to estimate the location and heat generation rate of the source from these temperature distributions, a genetic algorithm was used as the estimation method. The genetic algorithm utilizes a finite difference scheme for the direct solution of Pennes bioheat equation. It was determined that a genetic algorithm based approach is well suited for the estimation problem and that thermography can prove to be a valuable tool in locating tumors if combined with such an algorithm.

EXACT ANALYTICAL SOLUTION OF BIOHEAT EQUATION SUBJECTED TO INTENSIVE MOVING HEAT SOURCE

2017 ◽  
Vol 17 (05) ◽  
pp. 1750081 ◽  
Author(s):  
MOHAMMAD REZA TALAEE ◽  
ALI KABIRI
Keyword(s):  
Analytical Solution ◽  
Heat Source ◽  
Numerical Solutions ◽  
Exact Analytical Solution ◽  
Blood Perfusion ◽  
Temperature Profiles ◽  
Moving Heat Source ◽  
Bioheat Equation ◽  
Line Heat Source ◽  
Moving Line

Presented is the analytical solution of Pennes bio-heat equation, under localized moving heat source. The thermal behavior of one-dimensional (1D) nonhomogeneous layer of biological tissue is considered with blood perfusion term and modeled under the effect of concentric moving line heat source. The procedure of the solution is Eigen function expansion. The temperature profiles are calculated for three tissues of liver, kidney, and skin. Behavior of temperature profiles are studied parametrically due to the different moving speeds. The analytical solution can be used as a verification branch for studying the practical operations such as scanning laser treatment and other numerical solutions.

scholarly journals Data on Orientation to Happiness in Higher Education Institutions from Mexico and El Salvador

Data ◽  
2020 ◽  
Vol 5 (1) ◽  
pp. 27
Author(s):  
Domingo Villavicencio-Aguilar ◽  
Edgardo René Chacón-Andrade ◽  
Maria Fernanda Durón-Ramos
Keyword(s):  
Higher Education ◽  
El Salvador ◽  
Latin American ◽  
Higher Education Institutions ◽  
Two Dimensions ◽  
Three Dimensions ◽  
Stepwise Multiple Regression ◽  
Teacher Student ◽  
And Gender ◽  
Student’S T

Happiness-oriented people are vital in every society; this is a construct formed by three different types of happiness: pleasure, meaning, and engagement, and it is considered as an indicator of mental health. This study aims to provide data on the levels of orientation to happiness in higher-education teachers and students. The present paper contains data about the perception of this positive aspect in two Latin American countries, Mexico and El Salvador. Structure instruments to measure the orientation to happiness were administrated to 397 teachers and 260 students. This data descriptor presents descriptive statistics (mean, standard deviation), internal consistency (Cronbach’s alpha), and differences (Student’s t-test) presented by country, population (teacher/student), and gender of their orientation to happiness and its three dimensions: meaning, pleasure, and engagement. Stepwise-multiple-regression-analysis results are also presented. Results indicated that participants from both countries reported medium–high levels of meaning and engagement happiness; teachers reported higher levels than those of students in these two dimensions. Happiness resulting from pleasure activities was the least reported in general. Males and females presented very similar levels of orientation to happiness. Only the population (teacher/student) showed a predictive relationship with orientation to happiness; however, the model explained a small portion of variance in this variable, which indicated that other factors are more critical when promoting orientation to happiness in higher-education institutions.

scholarly journals Free partition functions and an averaged holographic duality

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Nima Afkhami-Jeddi ◽  
Henry Cohn ◽  
Thomas Hartman ◽  
Amirhossein Tajdini
Keyword(s):  
Partition Function ◽  
Spectral Gap ◽  
Central Charge ◽  
Three Dimensional ◽  
Two Dimensions ◽  
Three Dimensions ◽  
Partition Functions ◽  
General Constraints ◽  
Dimensional Gravity ◽  
Holographic Duality

Abstract We study the torus partition functions of free bosonic CFTs in two dimensions. Integrating over Narain moduli defines an ensemble-averaged free CFT. We calculate the averaged partition function and show that it can be reinterpreted as a sum over topologies in three dimensions. This result leads us to conjecture that an averaged free CFT in two dimensions is holographically dual to an exotic theory of three-dimensional gravity with U(1)c×U(1)c symmetry and a composite boundary graviton. Additionally, for small central charge c, we obtain general constraints on the spectral gap of free CFTs using the spinning modular bootstrap, construct examples of Narain compactifications with a large gap, and find an analytic bootstrap functional corresponding to a single self-dual boson.

Turbulent three-dimensional dielectric electrohydrodynamic convection between two plates

2012 ◽  
Vol 696 ◽  
pp. 228-262 ◽  
Author(s):  
A. Kourmatzis ◽  
J. S. Shrimpton
Keyword(s):  
Spatial Data ◽  
Three Dimensional ◽  
Reynolds Numbers ◽  
Two Dimensions ◽  
Three Dimensions ◽  
Energy Budgets ◽  
Turbulent Regime ◽  
Scalar Flux ◽  
Wide Range ◽  
Scalar Variance

AbstractThe fundamental mechanisms responsible for the creation of electrohydrodynamically driven roll structures in free electroconvection between two plates are analysed with reference to traditional Rayleigh–Bénard convection (RBC). Previously available knowledge limited to two dimensions is extended to three-dimensions, and a wide range of electric Reynolds numbers is analysed, extending into a fully inherently three-dimensional turbulent regime. Results reveal that structures appearing in three-dimensional electrohydrodynamics (EHD) are similar to those observed for RBC, and while two-dimensional EHD results bear some similarities with the three-dimensional results there are distinct differences. Analysis of two-point correlations and integral length scales show that full three-dimensional electroconvection is more chaotic than in two dimensions and this is also noted by qualitatively observing the roll structures that arise for both low (${\mathit{Re}}_{E} = 1$) and high electric Reynolds numbers (up to ${\mathit{Re}}_{E} = 120$). Furthermore, calculations of mean profiles and second-order moments along with energy budgets and spectra have examined the validity of neglecting the fluctuating electric field ${ E}_{i}^{\ensuremath{\prime} } $ in the Reynolds-averaged EHD equations and provide insight into the generation and transport mechanisms of turbulent EHD. Spectral and spatial data clearly indicate how fluctuating energy is transferred from electrical to hydrodynamic forms, on moving through the domain away from the charging electrode. It is shown that ${ E}_{i}^{\ensuremath{\prime} } $ is not negligible close to the walls and terms acting as sources and sinks in the turbulent kinetic energy, turbulent scalar flux and turbulent scalar variance equations are examined. Profiles of hydrodynamic terms in the budgets resemble those in the literature for RBC; however there are terms specific to EHD that are significant, indicating that the transfer of energy in EHD is also attributed to further electrodynamic terms and a strong coupling exists between the charge flux and variance, due to the ionic drift term.

scholarly journals Analytical solution of one-dimensional Pennes’ bioheat equation

Open Physics ◽  
2020 ◽  
Vol 18 (1) ◽  
pp. 1084-1092
Author(s):  
Hongyun Wang ◽  
Wesley A. Burgei ◽  
Hong Zhou
Keyword(s):  
Analytical Solution ◽  
Radiofrequency Energy ◽  
Bioheat Equation ◽  
Surface Cooling ◽  
One Dimensional ◽  
The Fourier Transform ◽  
The One ◽  
Parameter Values ◽  
Mathematical Derivation ◽  
Effect Of Surface

Abstract Pennes’ bioheat equation is the most widely used thermal model for studying heat transfer in biological systems exposed to radiofrequency energy. In their article, “Effect of Surface Cooling and Blood Flow on the Microwave Heating of Tissue,” Foster et al. published an analytical solution to the one-dimensional (1-D) problem, obtained using the Fourier transform. However, their article did not offer any details of the derivation. In this work, we revisit the 1-D problem and provide a comprehensive mathematical derivation of an analytical solution. Our result corrects an error in Foster’s solution which might be a typo in their article. Unlike Foster et al., we integrate the partial differential equation directly. The expression of solution has several apparent singularities for certain parameter values where the physical problem is not expected to be singular. We show that all these singularities are removable, and we derive alternative non-singular formulas. Finally, we extend our analysis to write out an analytical solution of the 1-D bioheat equation for the case of multiple electromagnetic heating pulses.

scholarly journals On the forces that cable webs under tension can support and how to design cable webs to channel stresses

2019 ◽  
Vol 475 (2223) ◽  
pp. 20180781 ◽  
Author(s):  
Guy Bouchitté ◽  
Ornella Mattei ◽  
Graeme W. Milton ◽  
Pierre Seppecher
Keyword(s):  
Linear Programming ◽  
Convex Hull ◽  
Structural Engineering ◽  
Three Dimensional ◽  
Two Dimensions ◽  
Three Dimensions ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Finite Dimensional ◽  
Necessary And Sufficient

In many applications of structural engineering, the following question arises: given a set of forces f 1 ,  f 2 , …,  f N applied at prescribed points x 1 ,  x 2 , …,  x N , under what constraints on the forces does there exist a truss structure (or wire web) with all elements under tension that supports these forces? Here we provide answer to such a question for any configuration of the terminal points x 1 ,  x 2 , …,  x N in the two- and three-dimensional cases. Specifically, the existence of a web is guaranteed by a necessary and sufficient condition on the loading which corresponds to a finite dimensional linear programming problem. In two dimensions, we show that any such web can be replaced by one in which there are at most P elementary loops, where elementary means that the loop cannot be subdivided into subloops, and where P is the number of forces f 1 ,  f 2 , …,  f N applied at points strictly within the convex hull of x 1 ,  x 2 , …,  x N . In three dimensions, we show that, by slightly perturbing f 1 ,  f 2 , …,  f N , there exists a uniloadable web supporting this loading. Uniloadable means it supports this loading and all positive multiples of it, but not any other loading. Uniloadable webs provide a mechanism for channelling stress in desired ways.

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