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Computerized morphonuclear cell image analyses of malignant disease in bladder tissues.

We analyzed the relationship between several morphonuclear parameters related to nuclear size, densitometry (deoxyribonucleic acid content and ploidy) and the chromatin pattern versus the histopathological grading of 46 bladder cancer samples graded according to the World Health Organization classification. We used a SAMBA 200 cell image processor with software allowing for the discrimination of 15 different parameters on Feulgen-stained imprint smears. In addition, we set up preliminary data banks that enable objective and reproducible grading of unknown cases. This approach must be validated in a large series of cases to create an expert system for bladder malignancy diagnosis.

Cell Division

NLMEM: a new SAS/IML macro for hierarchical nonlinear models.

Analysis of longitudinal data is one of the most challenging tasks in statistical modeling. In the analysis, it is often necessary to take into account nonlinear response to a set of parameters of interest and correlation between measurements taken from the same individual. In addition, between- and within-subject variation has to be handled properly. An example of addressing these issues is the hierarchical nonlinear model, where parameter estimation can be performed using linearization method. In this paper a new NLMEM SAS/IML macro for hierarchical nonlinear models is proposed. The program uses a portion of the code developed earlier in NLINMIX. NLMEM retains all the benefits of NLINMIX while allowing the systematic part of the model structure to be specified using IML syntax. Consequently, NLMEM allows estimation of models which are not tractable using NLINMIX. In particular, it allows us to address advanced population pharmacokinetics and pharmacodynamics models specified by ordinary differential equations.

Computer Simulation

The biometrical comparison of cardiac imaging methods.

OBJECTIVES: Biometrical comparison procedures for cardiac imaging methods with continuous outcome are reviewed mainly concentrating on assessment and design adequate comparison of accuracy and precision. Univariate graphical and numerical representation of corresponding deviations is outlined to derive a 'check list' of minimum information necessary to compare the measurement methods. DATA: The methods reviewed here are illustrated by the comparison of standard 2DE bidimensional cardial volumetry versus assessment using TDE colour imaging in 28 normal probands. SOURCES: The paired t-test and the corresponding confidence interval approach are used to assess deviations in location of two imaging methods; the test procedures of Maloney and Rastogi Hahn and Nelson and Grubbs are surveyed as proposals for the comparison of precisions in paired data. The Krippendorff coefficient and the Bradley/Blackwood test are illustrated as surrogate measures for method concordance. CONCLUSIONS: Since these methods can be performed by simple modification of standard options available in most statistics software packages, this review intends to enable cardiologists to choose appropriate methods for statistical data analysis and representation on their own.

Biometry

Numerical evaluation of the production of radionuclides in a nuclear reactor (Part II).

A computer program called LAURA has been developed to predict the production rates of any member of a nuclei network undergoing spontaneous decay and/or induced neutron transformation in a nuclear reactor. The theoretical bases for the development of LAURA were discussed in Part I. In particular, in Part I, we described how an expression based on the Rubinson (1949) approach is used to evaluate the depletion function. In this paper (Part II), we describe the full simulation of radionuclide production including the decomposition of a reaction network into independent linear chains, provisions for periodic reactor shutdown and restart, and implementation of an approximate solution given by Raykin and Shlyakhter (1989) to account for the effect of feedback due to alpha decay. Also included are some examples which demonstrate possible uses for LAURA.

Computer Simulation

Compensation for displacement of the focal point in cone beam single photon emission computed tomography reconstruction.

This study examined the effects of focal point displacement on image quality in cone beam single photon emission computed tomography (SPECT). A new image reconstruction algorithm that accounts for the focal point shift was derived and three shift geometries were investigated. The geometries included a lateral shift with a fixed focal length but off-center focusing, a linear axial shift with a variable focal length that depends linearly on the distance between a bin of the detector and the center of the detector, and a random axial shift with a randomly varying focal length. Computer simulation was conducted to evaluate the shift effects with a phantom that was composed of 118 small spherical sources. The results demonstrated that the lateral shift of the focal point was more critical to image quality than was the axial shift. With a 0.64 cm (1 pixel) lateral shift, noticeable artifacts was observed, while an axial shift resulted in minimal changes in image quality until it reached 8 cm (12.5 pixels). The derived reconstruction algorithm eliminated most of the artifacts caused by a fixed lateral shift or a linear axial shift of the focal point, but failed to do so for a random axial shift since the linear distribution assumed in image reconstruction did not match the random shift occurred in acquisition of the data.

Algorithms

Statistical clustering techniques for the analysis of long molecular dynamics trajectories: analysis of 2.2-ns trajectories of YPGDV.

The microscopic interactions and mechanisms leading to nascent protein folding events are generally unknown. While such short time-scale events are difficult to study experimentally, molecular dynamics simulations of peptides can provide a useful model for studying events related to protein folding initiation. Recently, two extremely long molecular dynamics simulations (2.2 ns each) were carried out on the pentapeptide Tyr-Pro-Gly-Asp-Val [Tobias, D. J., Mertz, J. E., & Brooks, C. L., III (1991) Biochemistry 30, 6054-6058] that forms stable reverse turns in solution. Tobias et al. examined folding events in this large system (approximately 30,000 conformations) using traditional methods of trajectory analysis. The shear magnitude of this problem prompted us to develop an automated approach, based on self-organizing neural nets, to extract the key features of the molecular dynamics trajectory. The neural net is used to perform conformational clustering, which reduces the complexity of a system while minimizing the loss of information. The conformations were grouped together using distances in dihedral angle space as a measure of conformational similarity. The resulting clusters represent "conformational states", and transitions between these states were examined to identify mechanisms of conformational change. Many conformational changes involved the rotation of only a single dihedral angle, but concerted angle changes were also found. Most of the conformational information in the 30,000 samples from the full trajectories was retained in the relatively few resultant clusters, providing a powerful tool for analysis of an expanding base of large molecular simulations.

Algorithms

Oligomerization of the amide sensor protein AmiC by x-ray and neutron scattering and molecular modeling.

AmiC is the negative regulator of the amidase operon which is involved in amide metabolism in the cytosol of Pseudomonas aeruginosa. Crystal structures show that AmiC contains two large domains that are very similar to the periplasmic leucine-isoleucine-valine binding protein (LivJ) of Escherichia coli. Synchrotron X-ray and neutron (in 100% 2H2O buffer) scattering data were obtained for AmiC in the presence of its substrate acetamide and its anti-inducer butyramide which binds more weakly to AmiC than acetamide. Guinier analyses to obtain radius of gyration RG and molecular weight Mr values showed that AmiC formed trimers whose formation was favored in the presence of acetamide and which exhibited concentration-dependent properties at concentrations between 0.4 and 2 mg/mL. Above 2 mg/mL, where trimers predominated, the RG data were identical within 0.05 nm for AmiC-acetamide and AmiC-butyramide with mean X-ray and neutron RG values of 3.35 and 3. 28 nm, respectively. Scattering curve fits constrained by the crystal structure of AmiC-acetamide were evaluated in order to describe a model for trimeric AmiC. A translational search of parallel alignments of three monomers to form a symmetric AmiC homotrimer gave a good X-ray curve fit. Combinations of calculated curves for monomeric, dimeric, trimeric, and tetrameric AmiC as seen in the crystal structure of AmiC gave reasonable but weaker X-ray curve fits which did not favor the existence of tetrameric AmiC. It is concluded that AmiC exhibits novel ligand-dependent oligomerization properties in solution when these are compared to other members of the periplasmic binding protein superfamily, where AmiC exists in monomeric and trimeric forms, the proportions of which depend on the presence of acetamide or butyramide.

Bacterial Proteins

Mean residence times and distribution volumes for drugs undergoing linear reversible metabolism and tissue distribution and linear or nonlinear elimination from the central compartments.

Equations for the mean residence times in the body (MRT) and in the central compartment (MRTc) are derived for bolus central dosing of a drug and its metabolite which undergo linear tissue distribution and linear reversible metabolism but are eliminated either linearly or nonlinearly (Michaelis-Menten kinetics) from the central compartments. In addition, a new approach to calculate the steady-state volumes of distribution for nonlinear systems (reversible or nonreversible) is proposed based on disposition decomposition analysis. The application of these equations to a dual reversible two-compartment model is illustrated by computer simulations.

Computer Simulation

Influence of surface free energies and cohesion parameters on pharmaceutical material interaction parameters-theoretical simulations.

PURPOSE: The aim of this study was to perform simulations of the influence of surface free energies and cohesion parameters on various interaction parameters within binary systems. METHODS: Using predictive equations derived from surface free energies and cohesion parameters originally proposed by Wu (2, 3) and by Rowe (4), values of interfacial tension, spreading and reduced spreading coefficients, interaction parameter and strength of interaction were simulated by means of a data processor. The influence of polar and disperse fractions of the two interacting materials was also examined. RESULTS: From the simulations, boundary conditions could be drawn: minimum interfacial tension, positive spreading coefficient, reduced spreading coefficient superior to unity, maximum value of the interaction parameter or of the strength of interaction. CONCLUSIONS: Simulations of the various parameters will help the formulator to select proper materials, eg. an agent that will efficiently bind some powdered substrate, a film-forming agent that will properly coat given cores or a material that will enhibit high interaction with a substrate.

Biocompatible Materials

Bayesian population pharmacokinetic and pharmacodynamic analyses using mixture models.

Population studies of the pharmacokinetics or pharmacodynamics of drugs help us, learn about the variability in drug disposition and effects, information that can be used to treat future patients at safe and effective doses. We present a new approach to population modeling based on a weighted mixture of normal distributions having random weights and means. This method allows estimation of underlying continuous population distributions without prespecifying the parametric form or shape of these probability distributions. Additionally, this method can carry out nonparametric regression of pharmacokinetic or dynamic parameters on patient covariates while estimating the underlying distributions. Two examples illustrate the method and its flexibility.

Bayes Theorem

Internal packing conditions and fluctuations of amino acid residues in globular proteins.

In order to investigate the environmental conditions of amino acid residues in protein molecules, four kinds of packing studies (atomic, geometric, hydrophobic and hydration) were formulated and tested on two proteins; bovine pancreatic trypsin inhibitor (BPTI) and bovine pancreatic ribonuclease S (RNase S). The inter-relationship of these packings on the fluctuations of amino acid residues was analysed by comparing the packing results with the dynamical studies, such as the root-mean-square-deviation values of atomic displacements obtained from the trajectories of molecular dynamics simulation, temperature factor information from crystal structures and residue fluctuations in proteins from continuum model. These analyses yield information about the most fluctuating and most stabilizing residue sites. Comparison of the results obtained by these methods indicate a good agreement, specifying an inverse correlation between the residue packing and fluctuations. This kind of study is helpful in identifying the specific residue sites such as nucleation, receptor binding and antigenic determining sites which in a way indirectly correlates with the functional residues in protein molecules.

Amino Acids

Fast direct Fourier methods, based on one- and two-pass coordinate transformations, yield accurate reconstructions of x-ray CT clinical images.

The conversion from polar to Cartesian coordinates can be carried out with two-pass algorithms. The paper describes two different methods based on concentric square frames and octagonal frames and their results, obtained with accurate interpolations based on the "moving window Shannon reconstruction' (MWSR). The embedding of these algorithms in direct Fourier methods (DFMs) of tomographic reconstruction is discussed. With respect to one-pass methods and to the use of octagonal frames, the square frame method makes it possible to carry out the first pass, a radial resampling, in the direct space, before computing 1D Fourier transforms (FTs) of projections. Reconstructions of clinical images from the raw data of a third-generation x-ray tomograph are presented and compared with those obtained with one-pass DFMs and with the convolution back-projection method (CBPM) performed by the instrument. The simple algorithm using square frames yields results in complete agreement with other DFM protocols and the CBPM. On a general-purpose computer, the execution of DFM protocols based on one-pass and two-pass coordinate transformations is 35 to 55 times faster than the CBPM and make the algorithms attractive for modern instrumentation.

Algorithms

The relationship of intralaboratory bias and imprecision on laboratories' ability to meet medical usefulness limits.

The previously described computer modeling technic empirically develops quantitative relationships between intralaboratory performance, as characterized by individual laboratories' coefficients of variation (CVs) and biases, and clinical "medical usefulness limits." These limits determine the magnitude of total analytic error, the combined effects of CV and bias that can be tolerated by the clinician. The computer model delineates all combinations of CV and bias compatible with specified medical usefulness limits. Both CV and bias are critical in determining a laboratory's ability to meet medical usefulness limits. For example, a laboratory with a 6% CV and zero bias will meet the +/- 10% or less total analytic error (medical usefulness limit) 90% of the time. If the medical usefulness limit is expanded to +/- 15%, a laboratory with a 6% CV can tolerate coexisting relative biases of up to 4% and still meet this limit 95% of the time. Plots of the limiting values for combinations of intralaboratory CV and bias are given that allow the laboratory's results to fall within medical usefulness limits of 2, 5, 10, 15, and 20%.

Clinical Laboratory Techniques

Rapid numerical integration algorithm for finding the equilibrium state of a system of coupled binding reactions.

We have adapted a simple method of numerical integration to predict the equilibrium state of a population of components undergoing reversible association according to the Law of Mass Action. Its particular application is to populations of protein molecules in aqueous solution. The method is based on Euler integration but employs an adaptive step size: the time increment being reduced if it would make the concentration of any component negative and increased while the concentration of any component changes at greater than a specified rate. Parameters of the algorithm have been optimized empirically using a model set of binding equilibria with dissociation constants ranging from 10(-5) M to 10(-9) M. The method obtains the solution to a set of binding equilibria more rapidly than the conventional initial value methods (simple Euler, 4th order Runge-Kutta and variable-step Runge-Kutta methods were tested) for the same accuracy. A computer code in standard C is presented.

Algorithms

Bayesian inference on biopolymer models.

MOTIVATION: Most existing bioinformatics methods are limited to making point estimates of one variable, e.g. the optimal alignment, with fixed input values for all other variables, e.g. gap penalties and scoring matrices. While the requirement to specify parameters remains one of the more vexing issues in bioinformatics, it is a reflection of a larger issue: the need to broaden the view on statistical inference in bioinformatics. RESULTS: The assignment of probabilities for all possible values of all unknown variables in a problem in the form of a posterior distribution is the goal of Bayesian inference. Here we show how this goal can be achieved for most bioinformatics methods that use dynamic programming. Specifically, a tutorial style description of a Bayesian inference procedure for segmentation of a sequence based on the heterogeneity in its composition is given. In addition, full Bayesian inference algorithms for sequence alignment are described. AVAILABILITY: Software and a set of transparencies for a tutorial describing these ideas are available at http://www.wadsworth.org/res&res/bioinfo/

Bayes Theorem

Steady-state modelling of metabolic pathways: a guide for the prospective simulator.

Steady-state modelling and control analysis by means of computer simulation provides valuable insight into the behavior of metabolic pathways. This review, which is aimed at the newcomer to this field, discusses the objectives of steady-state modelling and the steady-state properties of the four basic metabolic structures, namely linear and branched chains, loops and cycles. It is shown how the model definition in terms of stoichiometric reactions and rate equations leads to a set of balance equations from which the conservation constraints and flux relationships can be deduced, either informally or through a rigorous analysis of the stoichiometric matrix. The initial analysis of a steady-state metabolic model is summarized in an algorithm. Key references to the literature on metabolic modelling are given.

Computer Simulation

The development of a high-order Taylor expansion solution to the chemical rate equation for the simulation of complex biochemical systems.

A numerical method for evaluating chemical rate equations is presented. This method was developed by expressing the system of coupled, first-degree, ordinary differential chemical rate equations as a single tensor equation. The tensorial rate equation is invariant in form for all reversible and irreversible reaction schemes that can be expressed as first- and second-order reaction steps, and can accommodate any number of reactive components. The tensor rate equation was manipulated to obtain a simple formula (in terms of rate constants and initial concentrations) for the power coefficients of the Taylor expansion of the chemical rate equation. The Taylor expansion formula was used to develop a FORTRAN algorithm for analysing the time development of chemical systems. A computational experiment was performed with a Michaelis-Menten scheme in which step size and expansion order (to the 100th term) were varied; the inclusion of high-order terms of the Taylor expansion was shown to reduce truncation and round-off errors associated with Runge-Kutta methods and lead to increased computational efficiency.

Algorithms

POLCA, a library running in a modern environment, implements a protocol for averaging randomly oriented images.

The library POLCA implements the averaging of biological structures whose images are recorded in digital form from electron micrographs. The averaging protocol is based upon a method developed about ten years ago, which allows one to operate on a sequence of objects oriented and displaced at random within their frame; the relative rotations and the displacements of the structures are detected with the use of correlation algorithms and modified to make all objects appear the same, apart from their noisy components. The average image is then obtained by a simple addition and the signal-to-noise ratio is improved by a factor equal to the square root of the number of objects used to calculate the average. With respect to the original implementation of the method, two novel features characterize the library: the first one deals with the functions that are cross-correlated to determine the relative rotations of the structures; the functions used here are the inverse transforms of the amplitude spectra (IAS functions), which give rise to sharp maxima when they are cross-correlated. The second peculiarity is the systematic adoption, in the transformations of coordinates and in other circumstances, of an interpolation technique based upon the Fourier series kernel. POLCA is written in C and runs on a VME machine under the UNIX V/68 operating system. A programming style has been adopted to exploit fully the machine resources.

Algorithms