A direct substitution, equation error technique for solving the thermographic tomography problem

A new technique for solving the combined state and parameter estimation problem in thermographic tomography is presented. The technique involves the direct substitution of known skin temperatures into the finite difference form of the bio-heat transfer equation as formulated for solving an initial value problem with a convection boundary condition at the skin surface. These equations are then used to solve the inverse bio-heat transfer problem for the unknown subcutaneous tissue temperatures and physiological parameters. For a small number of nodal points, closed form algebraic solutions are obtained. For larger sets of equations, a hybrid technique is used in which the problem is initially posed as an unconstrained optimization problem in which the model equation error is minimized using the conjugate gradient descent technique to get close to a solution. Then a generalized Newton-Raphson technique was used to solve the equations. A numerical simulation of a one-dimensional problem is investigated both with and without noise superimposed on the input (transient) skin temperature data. The results show that the technique gives very accurate results if the skin temperature data contains little noise. It is also shown that if the physical properties of the tissue and the metabolism are known, that a given set of proper transient skin temperature inputs yields a unique solution for the unknown internal temperatures and blood perfusion rates. However, the similar problem with known blood perfusion rates and unknown metabolisms does not yield a unique solution for the internal temperatures and metabolisms.     

Thermal detection of embedded tumors using infrared imaging

Breast cancer is the most common cancer among women. Thermography, also known as thermal or infrared imaging, is a procedure to determine if an abnormality is present in the breast tissue temperature distribution. This abnormality in temperature distribution might indicate the presence of an embedded tumor. Although thermography is currently used to indicate the presence of an abnormality, there are no standard procedures to interpret these and determine the location of an embedded tumor. This research is a first step towards this direction. It explores the relationship between the characteristics (location and power) of an embedded heat source and the resulting temperature distribution on the 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 the Pennes bioheat equation. It was determined that a genetic algorithm based approach is well suited for the estimation problem since both the depth and the heat generation rate of the heat source were accurately predicted.     

Variational problems for the canonical profiles

A noncontradictory formulation of the variational problem for a canonical profile is proposed that refines the problem posed by B.B. Kadomtsev for a circular plasma cylinder. The results are generalized to a toroidal plasma with an arbitrary cross section. For the problem in toroidal geometry, boundary conditions are proposed with which to single out the Kadomtsev-like solution (the canonical profile) from the solutions to the Euler equation. Canonical profiles for the L-and H-modes are constructed. For a number of interesting examples, it is numerically shown that the second variation of the magnetic energy functional is positive. The canonical profile transport model is outlined, and the relationship between the canonical, numerical, and experimental profiles in tokamaks is briefly discussed.     

Dispatching and Conflict-Free Routing of Automated Guided Vehicles: An Exact Approach

This article presents an exact solution approach for the problem of the simultaneous dispatching and conflict-free routing of automated guided vehicles. The vehicles carry out material handling tasks in a flexible manufacturing system (FMS). The objective is to minimize the costs related to the production delays. The approach is based on a set partitioning formulation. The proposed model is solved to optimality by a column generation method, which is embedded in a branch-and-cut exploration tree. The proposed model and solution methodology are tested on several scenarios with up to four vehicles in the manufacturing system. The results show that most of these scenarios can be solved to optimality in less than three minutes of computational time.     

Minimum drag shape of a semi-ellipsoid exposed to shear flow and its possible relation to the shape of endothelial cell

A semi-ellipsoid attached on a wall is considered as a model problem for the study of blood flow effect on the shape of an endothelial cell. Under the condition that the volume is fixed and one axis of the semi-ellipsoid is aligned to the flow direction, the shape for the minimum drag under the applied shear flow is determined. Both the analytical and numerical approaches are adopted for computation of the minimum drag shape. Since analytical solution is not available for the original model problem, analytical solution to a closely related problem is used to compute the approximate value of the drag force. Adopted is the classical result on the motion of an ellipsoidal particle in a viscous fluid [Jeffery, Proc. Roy. Soc. A (1922)]. To corroborate the analytically obtained results, the model problem has also been studied numerically by using the finite element method (FEM). The minimum drag shape predicted analytically by using Jeffery’s solution is (a,b,c) = (1.71, 0.67, 0.88), where a is the dimensionless semi-axis in the flow direction, b the height, and c the half width of the semi-ellipsoid. The numerical approach predicts the minimal drag shape as (a,b,c) = (1.96,0.64,0.80). This result obtained by the FEM method shows good agreement with the result obtained by the boundary integral method [Hazel and Pedley, Biophys. J. (2000)].     

The use of a syncytium model of the crystalline lens of the eye as a new tool to study the light flashes phenomenon seen by astronauts

A syncytium model to study some electrical properties of the eye is proposed to study the phenomenon of anomalous light flashes (LF) perceived by astronauts in orbit. The crystalline lens is modelled as an ellipsoidal syncytium with a variable relative dielectric constant. The corresponding mathematical model is a boundary value problem for a system of two coupled elliptic partial differential equations in the two unknown syncytial electrical potentials. A numerical method to compute an approximate solution of this mathematical model is used, and some numerical results are shown. The model can be regarded as a new tool to study the LF phenomenon. In particular, the energy lost in the syncytium by a transversing cosmic charged particle is calculated and the results obtained with the syncytium model are compared with those obtained using the previously available Geant 3.21 simulation program. In addition, the interaction of antimatter–syncytium is studied, and the Creme96 computer program is used to evaluate the cosmic ray fluxes encountered by the International Space Station in its standard mission.     

The one‐inflated positive Poisson mixture model for use in population size estimation

The one‐inflated positive Poisson mixture model (OIPPMM) is presented, for use as the truncated count model in Horvitz–Thompson estimation of an unknown population size. The OIPPMM offers a way to address two important features of some capture–recapture data: one‐inflation and unobserved heterogeneity. The OIPPMM provides markedly different results than some other popular estimators, and these other estimators can appear to be quite biased, or utterly fail due to the boundary problem, when the OIPPMM is the true data‐generating process. In addition, the OIPPMM provides a solution to the boundary problem, by labelling any mixture components on the boundary instead as one‐inflation.     

BetaDock: shape-priority docking method based on beta-complex

This paper presents an approach and a software, BetaDock, to the docking problem by putting the priority on shape complementarity between a receptor and a ligand. The approach is based on the theory of the β-complex. Given the Voronoi diagram of the receptor whose topology is stored in the quasi-triangulation, the β-complex corresponding to water molecule is computed. Then, the boundary of the β-complex defines the β-shape which has the complete proximity information among all atoms on the receptor boundary. From the β-shape, we first compute pockets where the ligand may bind. Then, we quickly place the ligand within each pocket by solving the singular value decomposition problem and the assignment problem. Using the conformations of the ligands within the pockets as the initial solutions, we run the genetic algorithm to find the optimal solution for the docking problem. The performance of the proposed algorithm was verified through a benchmark test and showed that BetaDock is superior to a popular docking software AutoDock 4.     

An analytical study of cryosurgery in the lung.

The process of freezing in healthy lung tissue and in tumors in the lung during cryosurgery was modeled using one-dimensional close form techniques and finite difference techniques to determine the temperature profiles and the propagation of the freezing interface in the tissue. A thermal phenomenon was observed during freezing of lung tumors embedded in healthy tissue, (a) the freezing interface suddenly accelerates at the transition between the tumor and the healthy lung, (b) the frozen tumor temperature drops to low values once the freezing interface moves into the healthy lung, and (c) the outer boundary temperature has a point of sharp inflection corresponding to the time at which the tumor is completely frozen.     

BetaDock: Shape-Priority Docking Method Based on Beta-Complex

Abstract

This paper presents an approach and a software, BetaDock, to the docking problem by putting the priority on shape complementarity between a receptor and a ligand. The approach is based on the theory of the β-complex. Given the Voronoi diagram of the receptor whose topology is stored in the quasi-triangulation, the β-complex corresponding to water molecule is computed. Then, the boundary of the β-complex defines the β-shape which has the complete proximity information among all atoms on the receptor boundary. From the β-shape, we first compute pockets where the ligand may bind. Then, we quickly place the ligand within each pocket by solving the singular value decomposition problem and the assignment problem. Using the conformations of the ligands within the pockets as the initial solutions, we run the genetic algorithm to find the optimal solution for the docking problem. The performance of the proposed algorithm was verified through a benchmark test and showed that BetaDock is superior to a popular docking software AutoDock 4.     

Nonparametric Modeling of Longitudinal Covariance Structure in Functional Mapping of Quantitative Trait Loci

Summary Estimation of the covariance structure of longitudinal processes is a fundamental prerequisite for the practical deployment of functional mapping designed to study the genetic regulation and network of quantitative variation in dynamic complex traits. We present a nonparametric approach for estimating the covariance structure of a quantitative trait measured repeatedly at a series of time points. Specifically, we adopt Huang et al.'s (2006, Biometrika 93 , 85–98) approach of invoking the modified Cholesky decomposition and converting the problem into modeling a sequence of regressions of responses. A regularized covariance estimator is obtained using a normal penalized likelihood with an L₂ penalty. This approach, embedded within a mixture likelihood framework, leads to enhanced accuracy, precision, and flexibility of functional mapping while preserving its biological relevance. Simulation studies are performed to reveal the statistical properties and advantages of the proposed method. A real example from a mouse genome project is analyzed to illustrate the utilization of the methodology. The new method will provide a useful tool for genome‐wide scanning for the existence and distribution of quantitative trait loci underlying a dynamic trait important to agriculture, biology, and health sciences.     

Quantitative evaluation of the allometric transformation of of biological structures

Detection and quantification of allometry is a crucial problem in understanding morphological changes, both for systematic and morphogenetic purposes. A section of S.A.M. (Shape Analytical Morphometry) software system was used for this attempt. It consists of the following steps: a) boundary detection; b) starting point detection; c) size normalization; d) extraction of the fundamental shape by Kth order polynomials; e) finding of symmetry evaluator (S.A.E.) by means of a second degree equation. This last procedure gives an arc-chord complex that expresses a vector for allometry where intercept value was for application point, first degree coefficient was for direction and second degree coefficient was for modulus and versus. The main parameters, isometry fraction and allometry fraction may be understood referring them to morphogenetic models.     

A combined macro and microvascular model for whole limb heat transfer

A new prototype model for whole limb heat transfer is proposed wherein the countercurrent heat exchange from the large central arteries and veins in the core of the limb is coupled to microvascular models for the surrounding muscle and the cutaneous tissue layers. The local microvascular temperature field in the muscle tissue is described by the bioheat equation of Weinbaum and Jiji. The new model allows for an arbitrary axial variation of cross-sectional area and blood distribution between the muscle and cutaneous tissue, accounts for the blood flow to and heat loss from the hand and treats the venous return temperature and surface temperature distribution as unknowns that are determined as part of the solution to the overall boundary value problem. Representative solutions are presented for a wide range of environmental conditions for a limb in both the resting state and during exercise.     

Transient bioheat simulation of the laser-tissue interaction in human skin using hybrid finite element formulation

This paper presents a hybrid finite element model for describing quantitatively the thermal responses of skin tissue under laser irradiation. The model is based on the boundary integral-based finite element method and the Pennes bioheat transfer equation. In this study, temporal discretization of the bioheat system is first performed and leads to the well-known modified Helmholtz equation. A radial basis function approach and the boundary integral based finite element method are employed to obtain particular and homogeneous solutions of the laser-tissue interaction problem. In the boundary integral based finite element formulation, two independent fields are assumed: intra-element field and frame field. The intra-element field is approximated through a linear combination of fundamental solutions at a number of source points outside the element domain. The frame temperature field is expressed in terms of nodal temperature and the corresponding shape function. Numerical examples are considered to verify and assess the proposed numerical model. Sensitivity analysis is performed to explore the thermal effects of various control parameters on tissue temperature and to identify the degree of burn injury due to laser heating.     

Equilibrium electropotentials in electrolyte systems

The determinationof electric potentials in finite regions of symmetrical electrolyte in one-dimensional equilibrium situations requires the solution of the one-dimensional Poisson-Boltzmann equation in which the dependent variable is linearly related to the electric potential and contains unknown parameters. These require evaluation as part of the solution to a given boundary value problem. The general solution of the equation is presented. This involves elliptic functions and integrals and is sectionally isomorphic with respect to an integration parameter. The application to problems posed in terms of both initial values and two-point boundary values is discussed. The solution is used to determine the potential and concentration distributions between two flat-faced charged particles immersed in an electrolyte liquid and having interacting double layers.     

Shape information from shading: a theory about human perception

I present evidence that people assume a simple, linear reflectance function when interpreting shading information. Using this reflectance function I derive a closed-form solution to the problem of extracting shape information from image shading. The solution does not employ an assumption about surface smoothness and so is directly applicable to complex natural surfaces such as hair or cloth. A simple biological mechanism is proposed to implement this recovery of shape. It is shown that this simple mechanism can also extract significant shape information from line drawings.     

Numerical Solution to Generalized Burgers'-Fisher Equation Using Exp-Function Method Hybridized with Heuristic Computation

In this paper, a new heuristic scheme for the approximate solution of the generalized Burgers''-Fisher equation is proposed. The scheme is based on the hybridization of Exp-function method with nature inspired algorithm. The given nonlinear partial differential equation (NPDE) through substitution is converted into a nonlinear ordinary differential equation (NODE). The travelling wave solution is approximated by the Exp-function method with unknown parameters. The unknown parameters are estimated by transforming the NODE into an equivalent global error minimization problem by using a fitness function. The popular genetic algorithm (GA) is used to solve the minimization problem, and to achieve the unknown parameters. The proposed scheme is successfully implemented to solve the generalized Burgers''-Fisher equation. The comparison of numerical results with the exact solutions, and the solutions obtained using some traditional methods, including adomian decomposition method (ADM), homotopy perturbation method (HPM), and optimal homotopy asymptotic method (OHAM), show that the suggested scheme is fairly accurate and viable for solving such problems.     

Pattern recognition in several sequences: Consensus and alignment

The comparison of several sequences is central to many problems of molecular biology. Finding consensus patterns that define genetic control regions or that determine structural or functional themes are examples of these problems. Previously proposed methods, such as dynamic programming, are not adequate for solving problems of realistic size. This paper gives a new and practical solution for finding unknown patterns that occur imperfectly above a preset frequency. Algorithms for finding the patterns are given as well as estimates of statistical significance. This author supported by a grant from the System Development Foundation. This author supported by NSF grant MCS-8301960 and by a grant from the System Development Foundation. This author supported by NIH grant GM19036.     

The effect of geometry on tumor thermal profile and its use in tumor functional state estimation

Thermal differences between transplanted tumors and tumors in humans prevent the implementation of thermographic methods developed in mice models to human models and vise‐versa. Transplantable tumors tend to have an extruding shape, which may affect the thermal patterns. This hypothesis was studied in phantom experiments and simulations. A correlation between tumor dimensions and relative temperature was found and used to estimate tumor functional state from previously published in vivo experiments. A correlation was found between temperature differences and tumor growth rates (tumor aggressiveness) and the effect of tumor treatment was demonstrated, showing the potential for in vivo, non‐invasive tumor monitoring. (© 2015 WILEY‐VCH Verlag GmbH &Co. KGaA, Weinheim)     

Divisible Load Scheduling in Systems with Limited Memory

In this work we consider scheduling divisible loads on a distributed computing system with limited available memory. The communication delays and heterogeneity of the system are taken into account. The problem studied consists in finding such a distribution of the load that the communication and computation time is the shortest possible. A new robust method is proposed to solve the problem of finding optimal distribution of computations on star network, and networks in which binomial trees can be embedded (meshes, hypercubes, multistage interconnections). We demonstrate that in many cases memory limitations do not restrict efficiency of parallel processing as much as computation and communication speeds.