Program Code Generator for Cardiac Electrophysiology Simulation with Automatic PDE Boundary Condition Handling

Clinical and experimental studies involving human hearts can have certain limitations. Methods such as computer simulations can be an important alternative or supplemental tool. Physiological simulation at the tissue or organ level typically involves the handling of partial differential equations (PDEs). Boundary conditions and distributed parameters, such as those used in pharmacokinetics simulation, add to the complexity of the PDE solution. These factors can tailor PDE solutions and their corresponding program code to specific problems. Boundary condition and parameter changes in the customized code are usually prone to errors and time-consuming. We propose a general approach for handling PDEs and boundary conditions in computational models using a replacement scheme for discretization. This study is an extension of a program generator that we introduced in a previous publication. The program generator can generate code for multi-cell simulations of cardiac electrophysiology. Improvements to the system allow it to handle simultaneous equations in the biological function model as well as implicit PDE numerical schemes. The replacement scheme involves substituting all partial differential terms with numerical solution equations. Once the model and boundary equations are discretized with the numerical solution scheme, instances of the equations are generated to undergo dependency analysis. The result of the dependency analysis is then used to generate the program code. The resulting program code are in Java or C programming language. To validate the automatic handling of boundary conditions in the program code generator, we generated simulation code using the FHN, Luo-Rudy 1, and Hund-Rudy cell models and run cell-to-cell coupling and action potential propagation simulations. One of the simulations is based on a published experiment and simulation results are compared with the experimental data. We conclude that the proposed program code generator can be used to generate code for physiological simulations and provides a tool for studying cardiac electrophysiology.     

Straits used for international navigation

Abstract

This article summarizes our perspective of U.S. and Soviet interactions during a joint physical oceanography experiment. One author (RHH) was involved in early instrumentation and logistic work with the Soviets beginning in 1970, and was U.S. executive manager for the program from 1976–84. One author (CAC) was the National Science Foundation program manager responsible for administering the program. The experiment began with a preliminary meeting of Soviet and American oceanographers in 1973 and activities concluded with the publication of an atlas (see n. 9) in 1986. The intervening years included a variety of joint scientific activities which spanned a broad spectrum from theory and numerical modeling to at‐sea experiments. The total cost of U.S. activities as part of this program was about $25 million.     

A graphical user interface for BIOEQS: a program for simulating and analyzing complex biomolecular interactions

BIOEQS is a global analysis and simulation program for complex biomolecular interaction data developed during the 1990s. Its continued usefulness derives from the fact that it is based on a numerical solver for complex coupled biological equilibria rather than on closed-form analytical equations for the binding isotherms. Therefore, it is quite versatile, allowing easy testing of multiple binding models and analysis of systems too complex for closed-form solutions. However, a major drawback to a generalized use of this program has been the lack of a graphical user interface (GUI) for setting up the binding models and experimental conditions as well as for visualizing the results. We present here a new GUI for BIOEQS that should be useful in both research and teaching applications.     

A network thermodynamic method for numerical solution of the Nernst-Planck and Poisson equation system with application to ionic transport through membranes

Simple techniques of network thermodynamics are used to obtain the numerical solution of the Nernst-Planck and Poisson equation system. A network model for a particular physical situation, namely ionic transport through a thin membrane with simultaneous diffusion, convection and electric current, is proposed. Concentration and electric field profiles across the membrane, as well as diffusion potential, have been simulated using the electric circuit simulation program, SPICE. The method is quite general and extremely efficient, permitting treatments of multi-ion systems whatever the boundary and experimental conditions may be.     

Lord’s Paradox in a Continuous Setting and a Regression Artifact in Numerical Cognition Research

In this paper we review, and elaborate on, the literature on a regression artifact related to Lord’s paradox in a continuous setting. Specifically, the question is whether a continuous property of individuals predicts improvement from training between a pretest and a posttest. If the pretest score is included as a covariate, regression to the mean will lead to biased results if two critical conditions are satisfied: (1) the property is correlated with pretest scores and (2) pretest scores include random errors. We discuss how these conditions apply to the analysis in a published experimental study, the authors of which concluded that linearity of children’s estimations of numerical magnitudes predicts arithmetic learning from a training program. However, the two critical conditions were clearly met in that study. In a reanalysis we find that the bias in the method can fully account for the effect found in the original study. In other words, data are consistent with the null hypothesis that numerical magnitude estimations are unrelated to arithmetic learning.     

A computer program for the estimation of protein and nucleic acid sequence diversity in random point mutagenesis libraries

A computer program for the generation and analysis of in silico random point mutagenesis libraries is described. The program operates by mutagenizing an input nucleic acid sequence according to mutation parameters specified by the user for each sequence position and type of point mutation. The program can mimic almost any type of random mutagenesis library, including those produced via error-prone PCR (ep-PCR), mutator Escherichia coli strains, chemical mutagenesis, and doped or random oligonucleotide synthesis. The program analyzes the generated nucleic acid sequences and/or the associated protein library to produce several estimates of library diversity (number of unique sequences, point mutations, and single point mutants) and the rate of saturation of these diversities during experimental screening or selection of clones. This information allows one to select the optimal screen size for a given mutagenesis library, necessary to efficiently obtain a certain coverage of the sequence-space. The program also reports the abundance of each specific protein mutation at each sequence position, which is useful as a measure of the level and type of mutation bias in the library. Alternatively, one can use the program to evaluate the relative merits of preexisting libraries, or to examine various hypothetical mutation schemes to determine the optimal method for creating a library that serves the screen/selection of interest. Simulated libraries of at least 10⁹ sequences are accessible by the numerical algorithm with currently available personal computers; an analytical algorithm is also available which can rapidly calculate a subset of the numerical statistics in libraries of arbitrarily large size. A multi-type double-strand stochastic model of ep-PCR is developed in an appendix to demonstrate the applicability of the algorithm to amplifying mutagenesis procedures. Estimators of DNA polymerase mutation-type-specific error rates are derived using the model. Analyses of an alpha-synuclein ep-PCR library and NNS synthetic oligonucleotide libraries are given as examples.     

Distinction of microcytic disorders: comparison of expert, numerical-discriminant, and microcomputer analysis

Presumptive distinction between iron deficiency and heterozygous thalassemia by analysis of the automated blood count and differential continues to be a challenge. We compared two proposed numerical discriminants (MCV2 x MCH, and MCV2 x RDW/100 x Hb) with an analytic microcomputer program (BCDE2 Lea & Febiger). In 7114 subjects, the numerical discriminants and the BCDE2 program correctly identified greater than 90% of thalassemia. In subjects with iron deficiency, the BCDE program was greater than 90% sensitive and specific for positive identification, while the numerical discriminants were less than 75% sensitive and specific at inferential identification. The numerical discriminants, BCDE2, and 17 experts in blood counting were asked to interpret the blood-count data in 7 fully-defined actual cases. The mean experts' score was 5.65 cases correct out of 7. The BCDE program was correct in all cases. The numerical discriminants could not analyze all cases, and both were incorrect in at least one case. We conclude that for the task of analyzing blood counts for microcytic disorders, microcomputer analysis by BCDE outperforms both numerical discriminant functions and analysis by expert hematologists.     

Benchmark solution for the prediction of temperature distributions during radiofrequency ablation of cardiac tissue

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.     

A teaching exercise for the identification of bacteria using an interactive computer program

An interactive computer program written in Fortran is described which provides an exercise in the identification of bacteria. The program, IDEN, provides a novel way of enhancing a student's approach to systematic bacteriology and numerical identification procedures. An unknown bacterium is assigned to a student who is provided with a list of possible species and a list of tests which may be carried out. The student's objective is the correct identification of the unknown in the most economical manner. An indication is given concerning the way in which this program can be used to enhance theoretical instruction and practical investigation.     

Computer assisted floristic similarity analysis

A program for polythetic numerical evaluation of phytosociological material is described. Using Sörensen's coefficient of floristic similarity it computes the homogeneity of subjectively chosen sets of relevés, the affinity of each constituent relevé to the set as well as the similarity between any pair of sets. It is also able to plot a dendrogram of the hierarchic system obtained by agglomerating individual relevés into complex groupings. The program is suitable for processing phytosociological data arranged in any conventional table.     

Programs for evaluating and characterising bacterial taxonomic data

Three programs are described for evaluating and characterisingdata collected during numerical taxonomic studies of bacteria.The program VARIANCE compares replicate cultures and evaluatesthe reproducibility of each character. Also it identifies thosecharacters that should be excluded from subsequent taxonomicanalysis because of their poor reproducibility. GPROPS summarisesthe properties of clusters of strains that have been definedfrom a cluster analysis, it can produce a probabilistic identificationmatrix and compares each strain within a cluster with the HypotheticalMean Organism (HMO) of that cluster. OVCLUST is an implementationof the program described by Sneath (1979) which calculates overlapstatistics between major clusters. These programs are designedto complement the CLUSTAN package (Wishart, 1982) which is oftenused for cluster analysis of bacterial taxonomic data. The programswere written in FORTRAN 77 and implemented on an IBM PC usingMS–DOS. Received on November 13, 1986; accepted on January 8, 1987     

A numerical simulation of the flow in a T-type bifurcation and its application to an "end to side" fistula

Some recent surgical procedures such as arteriovenous fistula, or coronary and cerebral by-passes were observed to yield counterdirectional branching blood flows. There is a lack of knowledge about the role of the counterdirectional flow ratio, the angle of anastomosis and the shear stresses in the process of thrombogenesis that leads to shunt occlusion. The program developed to simulate these hemodynamic conditions uses an efficient numerical scheme for the solution of the 2-D Navier-Stokes equations and can be easily adapted to flows in other geometrical configurations.     

CDSpecTech: A single software suite for multiple chiroptical spectroscopic analyses

The program CDSpecTech was developed to facilitate the analysis of chiroptical spectra, which include the following: vibrational circular dichroism (VCD) and corresponding vibrational absorption (VA) spectra; vibrational Raman optical activity (VROA) and corresponding vibrational Raman spectra; electronic circular dichroism (ECD) and corresponding electronic absorption (EA) spectra. In addition, the program allows for generating optical rotatory dispersion (ORD) as the Kramers–Kronig transform of ECD spectra. The simulation of theoretical spectra from transition strengths can be achieved using different bandshape profiles. The experimental and simulated theoretical spectra can be visually compared by displaying them together. A unique feature of CDSpecTech is performing spectral analysis using the ratio spectra; i.e., the dimensionless dissymmetry factor (DF) spectrum, which is the ratio of CD to absorption spectra, and the dimensionless circular intensity difference (CID) spectrum, which is the ratio of VROA to vibrational Raman spectra. The quantitative agreement between experimental and simulated theoretical spectra can also be assessed from the numerical similarity overlap between them. Two different similarity overlap methods are available. The program uses a graphical user interface which allows for ease of use and facilitates the analysis. All these features make CDSpecTech a valuable tool for the analysis of chiroptical spectra. The program is freely available on the World Wide Web.     

The Routine Fitting of Kinetic Data to Models: A Mathematical Formalism for Digital Computers

A mathematical formalism is presented for use with digital computers to permit the routine fitting of data to physical and mathematical models. Given a set of data, the mathematical equations describing a model, initial conditions for an experiment, and initial estimates for the values of model parameters, the computer program automatically proceeds to obtain a least squares fit of the data by an iterative adjustment of the values of the parameters. When the experimental measures are linear combinations of functions, the linear coefficients for a least squares fit may also be calculated. The values of both the parameters of the model and the coefficients for the sum of functions may be unknown independent variables, unknown dependent variables, or known constants. In the case of dependence, only linear dependencies are provided for in routine use. The computer program includes a number of subroutines, each one of which performs a special task. This permits flexibility in choosing various types of solutions and procedures. One subroutine, for example, handles linear differential equations, another, special non-linear functions, etc. The use of analytic or numerical solutions of equations is possible.     

Parameter estimation for ligand binding systems kinetics applied to 1,25-dihydroxycholecalciferol

A mathematical analysis of the kinetics of the hormone-receptor interaction was applied to the 1,25-dihydroxycholecalciferol-intestinal receptor system. The exact analytical solution and the numerical integration of the kinetic equation were installed in a Statistical Analysis System (SAS) computer program to estimate the rate constants of the reaction. Estimates of the parameters obtained by these two methods are similar, demonstrating that the numerical integration can be combined with the nonlinear regression procedure for least-squares parameter fitting using a simple SAS program. This enables estimation of kinetics rate constants when the kinetic equation cannot be solved analytically. The ratio of the rate constants (ka/kd) found by the nonlinear procedure is close to the independently determined equilibrium (Scatchard) constant in the nonlinear analysis.     

Computer-based image analysis for the automated counting and morphological description of microalgae in culture

A largely unexplored area is the application of digital image processing to counting and sizing of microalgal cells from culture. Commercial systems are available, but have not been tested, nor necessarily optimized for high speed counting and sizing of phytoplankton. The present work describes the design, construction, specifications and comparative performance of an inexpensive system optimized for counting and sizing microalgal cells. This system has been tested with cells of the picoplankton to nanoplankton size ranges (1–20 μm). The hardware was a widely available standard microcomputer, an inexpensive video camera and monitor, and a video digitization board (frame grabber). A modifiable menu-driven program (PHYCOUNT) was written and provisions made to make this program available to other workers. The program is constructed such that it can be adapted to a variety of hardware setups Video digitization boards). Comparison of growth curves for microagae revealed there were no significant differences in division rate and cell yield as assessed by the image analysis method compared to manual counts with a hemacytometer. Several hundred cells were counted routinely within 10–15 s, far exceeding the counting rate achieved by hand tally. A variable transect feature allowed sampling every nth pixel and provided a substantial increase in execution speed. More than 1000 counts can be done per day. A protocol for the use of 96-well plates of polyvinyl chloride as counting chambers contributed to the processing of large numbers of samples rapidly. Other routines developed provided subtended area, defined the coordinates of cell perimeter, and derived cell length and width. The calculation of the latter two parameters was usually done off-line as data output is in standard numerical form accessible by other programs. Experience with daily use of the PHYCOUNT program and imaging hardware reveal that the system is reliable for cell counting and sizing. The presence of bacteria in the algal cultures does not affect cell counting or sizing.     

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.     

Analytical expressions for estimating endurance time and glove thermal resistance related to human finger in cold conditions

Frostbite is considered the severest form of cold injury and can lead to necrosis and loss of peripheral appendages. Therefore, prediction of endurance time of limb's tissue in cold condition is not only necessary but also crucial to estimate cold injury intensity and to choose appropriate clothing. According to the previous work which applied a 3-D thermal model for human finger to analyze cold stress, in this study, an expression is presented for endurance time in cold conditions to prevent cold injury. A formula is also recommended to select a proper glove with specific thermal resistance based on the ambient situation and cold exposure time. By employing linear extrapolation and real physical conditions, the proposed formulas were drawn out from numerical simulation. Analytical results show good agreement with numerical data. The used numerical data had been also validated with experimental data existed in the literature. Furthermore, the effect of different parameters such as glove thermal resistance and ambient temperature is investigated analytically.     

Thermal denaturation of double-stranded nucleic acids: prediction of temperatures critical for gradient gel electrophoresis and polymerase chain reaction.

A program is described which calculates the thermal stability and the denaturation behaviour of double-stranded DNAs and RNAs up to a length of 1000 base pairs. The algorithm is based on recursive generation of conditional and a priori probabilities for base stacking. Output of the program may be compared directly to experimental results; thus the program may be used to optimize the nucleic acid fragments, the primers and the experimental conditions prior to experiments like polymerase chain reactions, temperature-gradient gel electrophoresis, denaturing-gradient gel electrophoresis and hybridizations. The program is available in three versions; the first version runs interactively on VAXstations producing graphics output directly, the second is implemented as part of the HUSAR package at GENIUSnet, the third runs on any computer producing text output which serves as input to available graphics programs.     

Analytical Model for Estimating Terrestrial Cosmic Ray Fluxes Nearly Anytime and Anywhere in the World: Extension of PARMA/EXPACS

By extending our previously established model, here we present a new model called “PHITS-based Analytical Radiation Model in the Atmosphere (PARMA) version 3.0,” which can instantaneously estimate terrestrial cosmic ray fluxes of neutrons, protons, ions with charge up to 28 (Ni), muons, electrons, positrons, and photons nearly anytime and anywhere in the Earth’s atmosphere. The model comprises numerous analytical functions with parameters whose numerical values were fitted to reproduce the results of the extensive air shower (EAS) simulation performed by Particle and Heavy Ion Transport code System (PHITS). The accuracy of the EAS simulation was well verified using various experimental data, while that of PARMA3.0 was confirmed by the high R ² values of the fit. The models to be used for estimating radiation doses due to cosmic ray exposure, cosmic ray induced ionization rates, and count rates of neutron monitors were validated by investigating their capability to reproduce those quantities measured under various conditions. PARMA3.0 is available freely and is easy to use, as implemented in an open-access software program EXcel-based Program for Calculating Atmospheric Cosmic ray Spectrum (EXPACS). Because of these features, the new version of PARMA/EXPACS can be an important tool in various research fields such as geosciences, cosmic ray physics, and radiation research.