The Effects of Thermal Radiation on an Unsteady MHD Axisymmetric Stagnation-Point Flow over a Shrinking Sheet in Presence of Temperature Dependent Thermal Conductivity with Navier Slip

In this paper, the magnetohydrodynamic (MHD) axisymmetric stagnation-point flow of an unsteady and electrically conducting incompressible viscous fluid in with temperature dependent thermal conductivity, thermal radiation and Navier slip is investigated. The flow is due to a shrinking surface that is shrunk axisymmetrically in its own plane with a linear velocity. The magnetic field is imposed normally to the sheet. The model equations that describe this fluid flow are solved by using the spectral relaxation method. Here, heat transfer processes are discussed for two different types of wall heating; (a) a prescribed surface temperature and (b) a prescribed surface heat flux. We discuss and evaluate how the various parameters affect the fluid flow, heat transfer and the temperature field with the aid of different graphical presentations and tabulated results.     

Recent developments in methods for identifying reaction coordinates

In the study of rare events in complex systems with many degrees of freedom, a key element is to identify the reaction coordinates of a given process. Over recent years, a number of methods and protocols have been developed to extract the reaction coordinates based on limited information from molecular dynamics simulations. In this review, we provide a brief survey over a number of major methods developed in the past decade, some of which are discussed in greater detail, to provide an overview of the problems that are partially solved and challenges that still remain. A particular emphasis has been placed on methods for identifying reaction coordinates that are related to the committor.     

Theoretical analysis of thermal damage in biological tissues caused by laser irradiation

A bioheat transfer approach is proposed to study thermal damage in biological tissues caused by laser radiation. The laser light propagation in the tissue is first solved by using a robust seven-flux model in cylindrical coordinate system. The resulting spatial distribution of the absorbed laser energy is incorporated into the bioheat transfer equation for solving temperature response. Thermal damage to the tissue is assessed by the extent of denatured protein using a rate process equation. It is found that for the tissue studied, a significant protein denaturation process would take place when temperature exceeds about 53 degrees C. The effects of laser power, exposure time and beam size as well as the tissue absorption and scattering coefficients on the thermal damage process are examined and discussed. The laser conditions that cause irreversible damage to the tissue are also identified.     

Use of dual Euler angles to quantify the three-dimensional joint motion and its application to the ankle joint complex

This paper presents a modified Euler angles method, dual Euler angles approach, to describe general spatial human joint motions. In dual Euler angles approach, the three-dimensional joint motion is considered as three successive screw motions with respect to the axes of the moving segment coordinate system; accordingly, the screw motion displacements are represented by dual Euler angles. The algorithm for calculating dual Euler angles from coordinates of markers on the moving segment is also provided in this study. As an example, the proposed method is applied to describe motions of ankle joint complex during dorsiflexion–plantarflexion. A Flock of Birds electromagnetic tracking device (FOB) was used to measure joint motion in vivo. Preliminary accuracy tests on a gimbal structure demonstrate that the mean errors of dual Euler angles evaluated by using source data from FOB are less than 1° for rotations and 1 mm for translations, respectively. Based on the pilot study, FOB is feasible for quantifying human joint motions using dual Euler angles approach.     

A revised approach for an exact analytical solution for thermal response in biological tissues significant in therapeutic treatments

The genesis of the present research paper is to develop a revised exact analytical solution of thermal profile of 1-D Pennes’ bioheat equation (PBHE) for living tissues influenced in thermal therapeutic treatments. In order to illustrate the temperature distribution in living tissue both Fourier and non-Fourier model of 1-D PBHE has been solved by ‘Separation of variables’ technique. Till date most of the research works have been carried out with the constant initial steady temperature of tissue which is not at all relevant for the biological body due to its nonhomogeneous living cells. There should be a temperature variation in the body before the therapeutic treatment. Therefore, a coupled heat transfer in skin surface before therapeutic heating must be taken account for establishment of exact temperature propagation. This approach has not yet been considered in any research work. In this work, an initial condition for solving governing differential equation of heat conduction in biological tissues has been represented as a function of spatial coordinate. In a few research work, initial temperature distribution with PBHE has been coupled in such a way that it eliminates metabolic heat generation. The study has been devoted to establish the comparison of thermal profile between present approach and published theoretical approach for particular initial and boundary conditions inflicted in this investigation. It has been studied that maximum temperature difference of existing approach for Fourier temperature distribution is 19.6% while in case of non-Fourier, it is 52.8%. We have validated our present analysis with experimental results and it has been observed that the temperature response based on the spatial dependent variable initial condition matches more accurately than other approaches.     

Safe touch temperatures for hot plates.

A finite difference heat transfer model has been developed to predict the Safe Touch Temperatures (STT) for plates made of different materials. SST can be defined as the highest temperature at which no pain is felt when the surface is touched for a long enough period to allow safe handling of the equipment. The criterion used to quantify damage is the "damage function" that was originally proposed by Henriques and Moritz. There are several uncertainties present in the physiological and thermal properties of the skin that give rise to a solution range rather than a single solution. Certain simplifying assumptions are made that tend to yield solutions for STT that are toward the lower or "safe" end of the solution range. The model developed is a two-dimensional axisymmetric model in cylindrical coordinates. A finite difference scheme that uses the Alternating Direction Implicit method is used to solve the problem. It is a second-order scheme in both space and time domains. A parametric analysis of the model is performed to isolate those factors that affect the STT to the greatest extent. Data are presented for a variety of cases, which cover commonly observed ranges in material and geometric properties. It is found that the material properties, namely thermal conductivity and volumetric heat capacity, and the plate thickness ratio are the three most important parameters. These three parameters account for a range of STT from 56 degrees C-100 degrees C with thick metals at the low end and thin metals and plastics in the high range. This method represents a significant improvement over existing standard practices.     

Improved calculations of compactness and a reevaluation of continuous compact units

A new method for calculating compactness (Z) that uses look-up table-based algorithms for area and volume computations is introduced. These algorithms can be used in any iterative area orvolume calculation, are more than 1000 times faster than the originalalgorithms, and have equal or better precision. With the faster algorithms it is now possible to calculate the compactness of all continuous units in a protein, and to precisely locate the optimal compact units without the screening functions and limited resolution used previously. These methods have been incorporated into a fully automatic domain finding algorithm, and this method has been applied to the 21 proteins originally analyzed as well as 12 additional proteins. This method is robust, and yields similar units even when applied to coordinates of protein crystals grown under different experimental conditions. © 1993 Wiley-Liss, Inc.     

Idealized atomic coordinates of yeast phenylalanine transfer RNA.

The atomic coordinates are given for yeast phenylalanine transfer RNA in the orthorhombic crystal form. The structure has been refined by fitting to successively improved electron density maps at 2.7 Å resolution. The model fitting has been accomplished by using an interactive computer graphics system to minimize the errors inherent in manual model building and coordinate measurements, using an optical comparator. The atomic coordinates have then been “idealized” to make bond distances, bond angles, steric conformation and non-bonded contacts close to standard values, while constraining the model to fit the electron density maps.     

Simulation and investigation of quantum dot effects as internal heat-generator source in breast tumor site

The Pennes bio-heat transfer equation, which introduces the exchange magnitude of heat transfer between tissue and blood, is often used to solve the temperature distribution for thermal imaging and sensing. Near-infrared light has the ability to be used as a non-invasive means of diagnostic imaging within the woman's breast. Due to the diffusive nature of light in different tissue, computational model-based methods are required for functional imaging within the breast. In this article, the time-dependent bio-heat transfer is solved by a numerical method. In our model, the heat generation source (intrinsic and extrinsic) involves laser, metabolism, and quantum dot that the metabolism and heat generated by QDs are considered as intrinsic. We supposed the injected quantum dots would target the tumor site by a passive targeting process and then by interaction of laser radiation and quantum dot, the photoluminescence of quantum dot is converted to heat in the tumor site. The extra generated heat can impact on the extracted heat profile. One of the important applications of this research has led to a sensitivity improvement of the imaging system, which is potentially useful in the diagnosis and detection of breast cancer.     

Structures and analysis of highly homologous psychrophilic, mesophilic, and thermophilic adenylate kinases

The crystal structures of adenylate kinases from the psychrophile Bacillus globisporus and the mesophile Bacillus subtilis have been solved and compared with that from the thermophile Bacillus stearothermophilus. This is the first example we know of where a trio of protein structures has been solved that have the same number of amino acids and a high level of identity (66-74%) and yet come from organisms with different operating temperatures. The enzymes were characterized for their own thermal denaturation and inactivation, and they exhibited the same temperature preferences as their source organisms. The structures of the three highly homologous, dynamic proteins with different temperature-activity profiles provide an opportunity to explore a molecular mechanism of cold and heat adaptation. Their analysis suggests that the maintenance of the balance between stability and flexibility is crucial for proteins to function at their environmental temperatures, and it is achieved by the modification of intramolecular interactions in the process of temperature adaptation.     

A steep thermal gradient thermotaxis assay for the nematode Caenorhabditis elegans

The nematode Caenorhabditis elegans with its well-described nervous system is one of the multicellular organisms of choice to study thermotaxis. The neuronal circuitry for thermosensation has been analyzed at the level of individual cells. Two methods have previously been described to study the behavior of C. elegans with respect to temperature: 1) isothermal tracking assays and 2) linear thermal gradients (Hedgecock and Russell, 1975). Here we present a short linear thermal gradient assay which is faster and which allows statistical evaluation of different populations using a thermotaxis index. Thin agar plates are used on which a temperature gradient from about 10 degrees to 30 degrees is induced over the distance of about 5 cm. The short linear thermal gradient uses inexpensive materials so that multiple tests can be performed in parallel in a short period of time.     

Laser-induced hyperthermia of nanoshell mediated vascularized tissue – A numerical study

Laser-induced hyperthermia treatment of tumor in a 2-D axisymmetric tissue embedded with moderate size (100–150 µm) blood vessels is studied. Laser absorption is enhanced by embedding gold–silica nanoshells in the tumor. Heat transfer in the tissue is modeled using Weinbaum–Jiji bioheat transfer equation. With laser irradiation, the volumetric radiation is accounted in the governing bioheat equation. Radiative information needed in the bioheat equation is calculated using the discrete ordinate method, and the coupled bioheat-radiation equation is solved using the finite volume method. Effects of power density, laser exposure time, beam radius, diameter of blood vessel and volume fractions of nanoshells on temperature spread in the tissue are analyzed.     

Modeling of laser coagulation of tissue with MRI temperature monitoring

Light energy from a laser source that is delivered into body tissue via a fiber-optic probe with minimal invasiveness has been used to ablate solid tumors. This thermal coagulation process can be guided and monitored accurately by continuous magnetic resonance imaging (MRI) since the laser energy delivery system does not interfere with MRI. This report deals with mathematical modeling and analysis of laser coagulation of tissue. This model is intended for "real-time" analysis of magnetic resonance images obtained during the coagulation process to guide clinical treatment. A mathematical model is developed to simulate the thermal response of tissue to a laser light heating source. For fast simulation, an approximate solution of the thermal model is used to predict the dynamics of temperature distribution and tissue damage induced by a laser energy line source. The validity of these simulations is tested by comparison with MRI-based temperature data acquired from in vivo experiments in rabbits. The model-simulated temperature distribution and predicted lesion dynamics correspond closely with MRI-based data. These results demonstrate the potential for using this combination of fast modeling and MRI technologies during laser heating of tissue for online prediction of tumor lesion size during laser heating.     

A new pencil beam model for photon dose calculations in heterogeneous media

The pencil beam method is commonly used for dose calculations in intensity-modulated radiation therapy (IMRT). In this study, we have proposed a novel pencil model for calculating photon dose distributions in heterogeneous media. To avoid any oblique kernel-related bias and reduce computation time, dose distributions were computed in a spherical coordinate system based on the pencil kernels of different distances from source to surface (DSS). We employed two different dose calculation methods: the superposition method and the fast Fourier transform convolution (FFTC) method. In order to render the superposition method more accurate, we scaled the depth-directed component by moving the position of the entry point and altering the DSS value for a given beamlet. The lateral components were thus directly corrected by the density scaling method along the spherical shell without taking the densities from the previous layers into account. Significant computation time could be saved by performing the FFTC calculations on each spherical shell, disregarding density changes in the lateral direction. The proposed methods were tested on several phantoms, including lung- and bone-type heterogeneities. We compared them with Monte Carlo (MC) simulation for several field sizes with 6 MV photon beams. Our results revealed mean absolute deviations <1% for the proposed superposition method. Compared to the AAA algorithm, this method improved dose calculation accuracy by at least 0.3% in heterogeneous phantoms. The FFTC method was approximately 40 times faster than the superposition method. However, compared with MC, mean absolute deviations were <3% for the FFTC method.     

A relational database of protein structures designed for flexible enquiries about conformation

A relational database of protein structure has been developed to enable rapid and flexible enquiries about the occurrence of many aspects of protein architecture. The coordinates of 294 proteins from the Brookhaven Data Bank have been processed by standard computer programs to generate many additional terms that quantify aspects of protein structure. These terms include solvent accessibility, main-chain and side-chain dihedral angles, and secondary structure. In a relational database, the information is stored in tables with columns holding the different terms and rows holding the different entries for the terms. The different relational base tables store the information about the protein coordinate set, the different chains in the protein, the amino acid residues and ligands, the atomic coordinates, the salt bridges, the hydrogen bonds, the disulphide bridges and the close tertiary contacts. The database was established under ORACLE management system. Enquiries are constructed in ORACLE using SQL (structured query language) which is simple to use and alleviates the need for extensive computer programs. A single table can be searched for entries that meet various criteria, e.g. all protein solved to better than a given resolution. The power of the database occurs when several tables, or the entries in a single table, are cross-correlated. For example the dihedral angles of proline in the fourth position in an alpha-helix in high resolution structures can be rapidly obtained. The structural database provides a powerful tool to obtain empirical rules about protein conformation. This database of protein structures is part of a joint project between Birkbeck College and Leeds University to establish an integrated data resource of protein sequences and structures (ISIS) that encodes the complex patterns of residues and coordinates that define protein conformation. The entire data resource (ISIS) will provide a system to guide all areas of protein modelling including structure prediction, site-directed mutagenesis and de novo protein design. The availability of ISIS is described in the paper.     

Luminescent radio frequency radiation dosimetry

Thermoluminescent dosimetry has been the industry standard for ionizing radiation dosimetry because it is inexpensive, sensitive, and accurate. No such system exists for radio frequency radiation. This paper describes the state of the art of efforts toward developing such a system. Thermochemiluminescent (TCL) dosimetry, first reported in 1991, is a first step toward achieving this goal. However, it has had problems in the production of TCL materials and in conversion of the luminescent signal into specific absorption rate (SAR). The former problem has been solved by the development of a genetically engineered Escherichia coli bacterium (JM 109/plC20RNR_1.1), described herein, that produces the TCL material in a fermentation process. The latter problem stems from the difficulty in determining the structure of the currently best TCL material diazoluminomelanin. A theoretical approach for the solution of this problem has been achieved by combining equations for delayed fluorescence, temperature determination by TCL, and the free energy equation for equilibrium reactions. It has led to an explanation for the stable display of steady‐state energy disposition, illustrated by TCL, in phantoms without the expected disruption by thermal conduction or convection, at frequencies ranging from 2.06 GHz to 35 GHz. Bioelectromagnetics 20:46–51, 1999. Published 1999 Wiley‐Liss, Inc.     

Computation of steady flow in a two-dimensional arterial model

The Navier-Stokes equations are solved numerically for steady flow through a double-branched two-dimensional section of a three-dimensional model of a canine aorta for which experimental data is available. The numerical scheme involves transforming the physical coordinates to a curvilinear boundary-fitted coordinate system and performing finite-difference computations in the transformed system. Shear stress at the wall is calculated for a Reynolds number of a 1,000 with branch-to-main aortic flow rate ratios as a parameter. The results are compared with the aforementioned experimental data and show reasonable qualitative agreement.     

A procedure for determining angular positional data relative to the principal axes of the human body

This paper describes a simple computational procedure for determining angular displacement-time histories of human motion from three-dimensional cine data. The method is based on algebraic transformations of coordinates and coordinate axes. Through these coordinate transformations data was acquired for a multi-axial tumbling skill to illustrate angular displacement-time data relative to the moving coordinate system described by the human body through space.     

Single-file diffusion of uncharged particles

An equation for unidirectional fluxes of nonelectrolytes and for the total flux in the single-file transport through a narrow pore has been derived. The equation obtained accounts for the correlations of the population of the pore in the coordinate of transport. The problem has been solved using superposition approximation and unidirectional fluxes has been found. The population profile in the pore was shown to have nonlinear shape; this is principally different from the results of the classical diffusion approach.     

A Conjugate Thermo-Electric Model for a Composite Medium

Electrical transmission signals have been used for decades to characterize the internal structure of composite materials. We theoretically analyze the transmission of an electrical signal through a composite material which consists of two phases with different chemical compositions. We assume that the temperature of the biphasic system increases as a result of Joule heating and its electrical resistivity varies linearly with temperature; this last consideration leads to simultaneously study the electrical and thermal effects. We propose a nonlinear conjugate thermo-electric model, which is solved numerically to obtain the current density and temperature profiles for each phase. We study the effect of frequency, resistivities and thermal conductivities on the current density and temperature. We validate the prediction of the model with comparisons with experimental data obtained from rock characterization tests.