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Tooth surface fitting and three-dimensional display using hidden surface removal technique.

Bi-cubic parametric spline surface is applied for surface-fitting of the external surface and canal of tooth based on its crown-to-root, cross-sectional data obtained by X-ray scanning. For three-dimensional display of the fitted surfaces, a technique for fast removal of the hidden surfaces is also reported. The selection of the accumulated chord length or coordinate component as parameter make it possible to fit any kind of surface smoothly. For displaying or plotting a well-fitted surface, a method capable of discriminating the grades for sequential removal of the hidden surfaces is developed for substantial reduction of computing time.

Algorithms

Algorithms for the computation of spatial statistics.

Algorithms are described for the calculation of spatial statistics. The statistics are the functions K(t), G(y), F(x), and K12(t). They can be used to determine (a) which type of spatial process ('random', 'clustered', 'regular', etc.) best fits a data set and whether the spatial pattern changes with distance, and (b) whether two types of events are correlated with each other, and if so, at which distances the correlation occurs. These functions provide a powerful tool for analysing the spatial distribution of biomedical and biological phenomena. An interactive, command-driven program that incorporates these algorithms is described.

Algorithms

A program for simulation of nerve equations with branching geometries.

A computer program has been developed for simulation of electrical activity in neurons with complex branching morphology, multiple channel types, and inhomogeneous channel distribution. The program is based around an interpreter and screen editor for flexible specification of nerve properties and analysis of simulation results. Efficient simulation of the nerve specification is accomplished with procedure calls to fast, compiled routines for integration of the nerve equations.

Cell Membrane

High-precision three-dimensional photogrammetric calibration and object space reconstruction using a modified DLT-approach.

Two modified DLT algorithms are presented that improve the accuracy of three-dimensional object space reconstruction by almost an order of magnitude when compared with conventional methods. The improvement in the linear modified DLT (MDLT) algorithm is achieved by satisfying certain orthogonality conditions in the form of a non-linear constraint, thereby effectively eliminating a redundant DLT parameter. In the non-linear MDLT algorithm, the improvement and computational stability results from the appropriate elimination of implicit variables from one side of the approximating relations and the corresponding reformulation of the objective function to be minimized. The highest reconstruction accuracy of 0.733 mm rms mean error was obtained with the non-linear MDLT algorithm. This corresponds to a spatial resolution of about one part in 2860 or 0.035% overall accuracy. The accuracy obtainable with the linear MDLT was found to be slightly less and about 0.041% (0.833 mm rms mean error).

Algorithms

Intersection of shaped radiation beams with arbitrary image sections.

Display of the intersection of a shaped radiation beam with an arbitrarily oriented image plane is a very useful tool in three-dimensional external beam radiation treatment planning. Coverage of the tumor (or target) region can be graphically investigated, as well as the radiation received by the surrounding healthy tissues. An algorithm is presented that obtains and displays these intersections by projecting contour points defining the beam's aperture on the plane. A general procedure is given, as well as provisions for special cases in which a straightforward projection is not sufficient.

Algorithms

CONFREG: a BASIC program for calculating and plotting confidence regions based on correlational analyses.

Many observations encountered in biological and medical research are randomly distributed in bivariate scales, and thus not susceptible to simple regression analyses. Since such data are depicted by ellipses in scatter diagrams, a computer program to calculate the confidence regions for the means or the total data of bivariate samples was written in BASIC for correlational analyses. The program, based on the principal axes algorithm, plots the calculated confidence regions as an elliptic area, using the fitted equations for its major and minor axes. The program displays the sample parameters required to perform comparisons between different groups of experimental conditions.

Animals

BOOMER, a simulation and modeling program for pharmacokinetic and pharmacodynamic data analysis.

BOOMER is an improved version of an earlier non-linear regression program, MULTI-FORTE. Rather than the user writing a FORTRAN subroutine, models are defined by means of the parameters which make up the model. Models based on differential equations are specified by means of zero-order, first-order, or Michaelis-Menten-type rate constants. Doses (in units of mass) are translated into the usually observed concentration units by a reciprocal volume parameter. Integrated equation models are specified in terms of baseline terms, exponential terms, or the emax function with slope term as described by the Hill equation. Time points can be specified as parameters to specify dose times, infusion start/stop times, or lag times. With careful selection of parameters quite complex models can be specified. The user has a choice of differential equation solvers and fitting algorithms.

Computer Simulation

Evaluation of Monte Carlo generation of long-tailed symmetric and contaminated symmetric distributions.

Generating random variables from a specific distribution, whether symmetric or asymmetric, is a concern of investigators involved in Monte Carlo studies. Of particular interest to those concerned with robustness is the generation of contaminated symmetric distributions such as those used in the Princeton Robustness Study. A reliable composite uniform U(0,1) generator is described and algorithms for transforming U(0,1) to symmetric long-tailed and contaminated symmetric distributions are given. Goodness-of-fit tests and graphical illustrations demonstrate the adequacy of the empirical distributions.

Algorithms

An application of the D-optimal criterion to define the experimental design for a particular class of semi-parametric models.

An updated version of the computer program EXCAD [1] allows the user to optimize experimental design to estimate parameters of particular semi-parametric models. The semi-parametric models take the general form of a function of time (t): Y(t) = NL (c(t,alpha),beta). The function NL(C(t,alpha),beta), is, in general, a non-linear transformation of a function, C(t,alpha), that in turn is the convolution of two others. One of these two functions is expressed in a non-parametric form, and is not of direct interest to the experimenter. The other is of direct interest: it is a parametric function depending on a set of parameters alpha. This semi-parametric model applies to numerous kinds of biological experiments, such as pharmacokinetic/pharmacodynamic, physiological, circulatory flow experiments. This paper presents a new method for determining an optimal experimental design to estimate the parameters alpha and beta. The new approach adopts the D-optimal criterion, and is illustrated using real thiopental data.

Animals

A knowledge acquisition tool in analytical pathology based on multi-media relational database.

The need for a knowledge based expert system for efficient decision making in the field of pathology has been well accepted. To build the knowledge-base for such an expert system is a painstaking task. This work is an attempt to provide the pathologists a powerful and user-friendly tool that will help them in the process of building the knowledge-base for medical diagnosis by closely looking at the specimen images and their extracted feature values. The tool is based on multi-media relational database and software like VAX Rally (4GL), ILIAD and SAS to provide a wide-range comparative study between feature data and image data; and also their statistical analysis.

Artificial Intelligence

Correlation artifacts in speed of sound estimation in scattering media.

A recently described method for speed of sound estimation in tissues in pulse-echo mode involves reception of echoes generated by an ultrasonic pulse by means of a linearly tracking transducer. When the peaks of echo amplitudes are used as markers of arrival time, stairstep-like artifacts appear in the echo arrival time vs. transducer position plots. We postulate that these artifacts are a consequence of the speckle phenomenon commonly encountered in ultrasonic imaging. To test this hypothesis, we report computer simulations and water tank experiments which demonstrate similarities between the behavior of the stairsteps and the properties of ultrasonic speckle. Additionally, equations describing the precision of the speed of sound estimation in terms of the second order statistical properties of the stairstep artifact are derived.

Computer Simulation

Processing images of helical structures: a new twist.

Helical macromolecular assemblies are particularly difficult to study by X-ray diffraction but are quite well suited to analysis by electron microscopy. Most of our information about helical macromolecular assemblies has come from the electron microscope but has been limited to about 25 A resolution. With the use of low-dose electron cryomicroscopy, one can obtain structural data to near atomic resolution on two-dimensional crystals, but the problem is to extract the information from the noise. In this paper we present methods to extract signal from low-dose electron cryomicrographs of helically symmetric structures. We apply these methods to extract 10 A data from the bacterial flagellar filament.

Algorithms

Morphometric analysis of sonographic images by spatial geometric modeling.

A methodology able to derive spatial geometric models from input sequences of sonographic slices is proposed. The developed modeling procedure can be utilized to perform computer-assisted anatomic 3D analysis both on all echo space and selected subregions. The modeling procedure is mainly composed of three sequential phases: a) automatic acquisition and preprocessing of time sequences of 2D echotomograms; b) 3D reconstruction of images and computing of discrete distance maps of selected echoes according to predefined projective laws; and c) generation of a spatial geometric model of the examined object starting from the previously computed maps.

Algorithms

Determination of mean particle volume, a Monte Carlo simulation.

Either length measurements or area measurements may be made on a sample of profiles for the purpose of estimating the mean volume of a population of convex particles. Diameters of spheres, caliper diameters of ellipsoids and intercept lengths are available length measurements. Profile areas can be evaluated by planimetry or point counting. Either all the available profiles in random sections or point sampled profiles can be utilized. We have applied a Monte Carlo simulation to compare several of the stereologic methods for the estimation of the mean volumes of spheres and ellipsoids. Populations of spherical, prolate ellipsoidal and oblate ellipsoidal particles were subjected to random sectioning and measurement. Diameter, point sampled intercept length, area and point sampled area were measured in the case of the spherical particles. With the ellipsoids, the same measurement excepting diameters were performed. The measurements were converted to volumes by the appropriate equations, and the means, the standard deviations of the means and the 95% confidence intervals were determined for increasing sample sizes. All the methods provide estimates that converge on their theoretical mean volumes. The area measurements and particularly the point sampled area measurement show some advantage over the length measurements, but differences among the methods are small, not entirely consistent over the different cases and unlikely to be significant in most real applications.

Algorithms

Degenerate Hopf bifurcation and isolated periodic solutions of the Hodgkin-Huxley model with varying sodium ion concentration.

Points of degenerate Hopf bifurcation in the Hodgkin-Huxley model are found as parameters temperature T and voltage level of sodium VNa are varied. Local techniques of degenerate Hopf bifurcation analysis are used to show the existence of families of periodic solutions of the model: isolated branches of periodic solutions (i.e. branches not connected to the stationary branch) are found in addition to Hopf branches. Purely numerical techniques are used to show that the isolas persist for VNa up to a value slightly greater than 114 mV. Under some conditions there are multiple stable periodic solutions, so "jumping" between action potentials of different amplitudes might be observed.

Action Potentials