Time Interpolation Research Articles

977-71 Conduction Patterns of the Sinoatrial Node and Perinodal Region Demonstrated by an Optical Mapping Technique

Studies of the conduction patterns within the sinus node region have been limited to extracellular surface and intracellular microelectrode techniques. Even with multiple electrodes, data is limited to a finite number of discrete points within the tissue, thus pacemaker shifts, entrance block, and antegrade versus retrograde conduction differences have not been completely elucidated. To study the entire sinus node (SAN), functional perinodal boundary (FPB), and crista terminalis (CT) tissue preparation, we use a 144 element photodiode array recorded simultaneously with bipolar sensing and pacing electrograms. A wide margin of right atrial tissue including the interatrial septum (lAS), from an adult New Zealand white rabbit, was dissected and viability maintained by superfusion of 37°C, O 2 enriched Krebs. The tissue was stained with 2 mM di-4-ANEPPS, a voltage sensitive, optically active dye. The isochronal activation patterns are constructed by linear interpolation of times in the image space between photodiode elements (625 μm) . Each isochronal band represents 1 ms. conduction time. Single decremental premature stimuli (560 ms) were delivered into a sensed sinus rhythm (900 ms) at the inferior CT (STIM). Consistently, the premature stimulus shifts the slow conduction of the FPB medially toward the sinus node, increasing transverse conduction delay. This provokes rapid retrograde longitudinal conduction up the CT and preferentially enters the SAN within its superior margin. SAN depolarization then proceeds in a superior to inferior fashion. Premature depolarization of the superior margins of the SAN may offer explanations for sinoatrial entrance block and the superior shift in pacemaker site after early premature stimuli. Optical mapping may allow resolution of sinoatrial conduction physiology.

A high resolution and fast TDC for sensitive position gas-filled detectors

A time-to-digital converter has been developed for a gas filled detector with a delay line readout. It is based on a time interpolation method with a built-in master oscillator of 200 MHz. A resolution of 80 ps was achieved and the differential non linearity is less than ±1.5%. Also, a rate up to 3 MHz is possible. The circuit has a dynamic range of 16 bits and fed in a single width NIM format. The performance of the TDC and test results are given.

Use of Fourier transforms for asynoptic mapping: Applications to the upper atmosphere research satellite microwave limb sounder

Fourier analysis has been applied to data obtained from limb viewing instruments on the Upper Atmosphere Research Satellite. A coordinate system rotation facilitates the efficient computation of Fourier transforms in the temporal and longitudinal domains. Fields such as ozone (O3), chlorine monoxide (ClO), temperature, and water vapor have been transformed by this process. The transforms have been inverted to provide maps of these quantities at selected times, providing a method of accurate time interpolation. Maps obtained by this process show evidence of both horizontal and vertical transport of important trace species such as O3 and ClO. An examination of the polar regions indicates that large‐scale planetary variations are likely to play a significant role in transporting midstratospheric O3 into the polar regions. There is also evidence that downward transport occurs, providing a means of moving O3 into the polar vortex at lower altitudes. The transforms themselves show the structure and propagation characteristics of wave variations.

Stratospheric Analyses Produced by the United Kingdom Meteorological Office

Abstract Since late 1978, the U.K. Meteorological Office (UKMO) has processed accurate radiance measurements of the stratosphere from a set of three radiometers (Statospheric Sounding Unit, Microwave Sounding Unit, High-Resolution Infrared Sounder) flown on satellites in the TIROS series. The radiometers scan both sides of the subsatellite track giving almost global coverage. UKMO uses its own retrieval algorithm to derive thickness from radiances. The retrieval is a linear, physiral–statistical method that utilizes a reference set of temperature profiles as a priori data. Thickness are added to a contemporaneous field of geopotential height at 100 hPa to give geopotential heights at standard pressure levels in the stratosphere up to 1 hPa. Global synoptic fields for 1200 UTC are produced every day on a regular latitude–longitude grid by linear interpolation in space and time. The paper describes the retrieval method and objective analysis in detail. It outlines the availability of data in the 14-year arc...

Velocity distributions in the left ventricular outflow tract and the aortic anulus measured with Doppler colour flow mapping in normal subjects.

This study was designed to investigate the velocity distributions in the left ventricular outflow tract and aortic anulus. In 18 out of 22 healthy male individuals, instantaneous cross-sectional flow velocity profiles were constructed at different levels of the left ventricular outflow tract and aortic anulus by time interpolation of digital velocity data from sequentially delayed Doppler colour flow maps. The results showed that: (1) the velocity distributions in the left ventricular outflow tract and the aortic anulus were skewed with the highest velocities along the anterior and septal parts of the flow channel; (2) based on the time-velocity integral profiles in the aortic anulus, which were also skewed with the highest integrals along the anterior and septal parts, the maximal time-velocity integrals were higher than the mean cross-sectional time-velocity integrals by approximately 30% in the four chamber view and 40% in the long axis view. However, the time-velocity integrals at the middle point of the diameter correlated significantly with the mean cross-sectional time-velocity integrals in the four chamber view (10.3 +/- 0.8 vs 9.9 +/- 0.9 cm; r = 0.95) and in the long axis view (12.5 +/- 0.9 vs 11.8 +/- 0.8 cm; r = 0.95). Therefore, it can be concluded that: (1) the velocity distributions in the left ventricular outflow tract and the aortic anulus are skewed; (2) if the aortic anulus is used for cardiac output measurement by pulsed Doppler echocardiography in normal subjects, the middle point of its diameter is the best sampling site.

A diffusion wave finite element model for channel networks

A computational algorithm for the solution of prismatic dendritic channel networks based on the diffusion wave approximation of channel flow is presented. Finite elements are used for the spatial approximation and an implicit linear time interpolation scheme is used for the temporal discretization of the diffusion wave equations. The implicit scheme results in a system of nonlinear algebraic equations, which are iteratively evaluated using successive substitution. This scheme does not require any system matrix updates of the symmetric and banded algebraic equations. A second iteration scheme is used to model the network junction point boundary conditions, which allows each channel segment to be independently discretized and evaluated.This approach significantly reduces the storage and matrix decomposition requirements in the solution of a channel network system. An adaptive time incrementation scheme, which strives to achieve constancy in the number of junction point boundary condition iterations, is presented. The model routes a specified set of hydrographs through the channel network, as well as any specified lateral inflow into the channel. Results are presented for an example of a dendritic network, using rectangular and trapezoidal channel geometries.

Occultations of asteroids by the moon in 1992 and 1993

Predictions are given for the occultations of brighter asteroids by the Moon in 1992 and 1993. The predictions are based on the lunar ephemeris ELP 2000-85 (Chapront-Touze & Chapront, 1988, A & A, 190) and the osculating elements of numbered minor planets (Batrakov et al., 1991, Ephemerides of Minor Planets). They include only optically observable events, i.e., disappearances or reappearances at the dark lunar limb. The given ground tracks for promising events enable a coarse interpolation of the occultation time

A METHOD FOR PREDICTING AND MINIMIZING NUMERICAL DIFFUSION

Finite-difference numerical techniques based on control volumes provide the most commonly applied method for solution of heat and mass transfer problems. These first-order solutions are prone to substantial inaccuracy introduced by numerical diffusion effects, From a Lagrangian viewpoint, the inaccuracy of interpolation in space and time creates this diffusion. Here, Taylor series expansions for streamwise and cross-stream interpolation processes give numerical diffusion coefficients. These simple coefficients can be used to adjust physical diffusion coefficients, providing second-order accuracy for convection in control volume solutions. The diffusion correction functions derived here are particularly useful for transient solutions.

Impact of changes in heart rate and stroke volume on the cross sectional flow velocity distribution of diastolic mitral blood flow. A study on 6 patients with pacemakers programmed at different heart rates.

The effect of changes in stroke volume on the cross sectional velocity distribution in the mitral orifice during passive mitral inflow was studied in six patients with total atrioventricular block, atrial fibrillation and VVI pacemakers during periods with different heart rates. The time velocity integrals recorded both in the left ventricular outflow tract and at the mitral orifice decreased significantly as the heart rate was increased from 60 to 80 and from 80 to 100 beats per minute. Instantaneous cross sectional flow velocity profiles were constructed by time interpolation of the velocity data from each point in sequentially delayed two dimensional digital ultrasound maps. Each patient had a characteristic cross sectional flow velocity profile in the mitral orifice recorded at the level of the leaflet tips in a four chamber view. The velocity profiles varied between the patients. With increase in heart rate only minimal changes in the flow profiles from individual patients were seen. The maximum velocity through the mitral orifice overestimated the cross sectional mean velocity at the same time by a factor of 1.4-1.9. The maximum time velocity integral overestimated the cross sectional mean by a factor of 1.4-1.8. The observed cross sectional skew varied between patients but did not change significantly with increasing heart rate and decrease in stroke volume.

3D Reservoir Visualization

Summary This paper shows how some simple 3D graphics tools can be combined to provide efficient soft-ware for visualizing and analyzing data obtained from reservoir simulators and geological simulations. The animation and interactive capabilities of the software quickly provide a deep understanding of the fluid-flow behavior and an accurate idea of the internal architecture of a reservoir. Introduction Reservoir geologists and engineers often deal with 3D data from simulation programs. These data may represent lithofacies programs. These data may represent lithofacies or petrophysical values in 3D space. Some data may also vary in time. Without an adaptable way to represent-these numbers, it is difficult to understand their underlying physical phenomena in depth. Without physical phenomena in depth. Without visualization tools one must imagine a complex 3D structure (e.g., the architecture of a reservoir) or try to understand a movement within this structure (e.g., the fluid flow). We describe a software environment that allows scientists to explore, manipulate, and visualize their data interactively and dynamically on a workstation. With this software, the user can view precomputed data from any angle, can sort through the volume of data, and can even see a film from the data, if these data are evolving in time. Our aim is not to make general-purpose graphics software for visualization of data from molecular chemistry, computational fluid dynamics, or oil reservoir engineering. Our concern is to provide reservoir-simulation, reservoir-geology, and basin-modeling scientists with attractive, standard, 3D-graphics tools that meet their specific needs. Examples of the specific needs encountered are described below. To handle lithofacies and petrophysical values, we introduce the distinction between discrete and continuous scalars; i.e., no interpolation between data is required for discrete scalars (interpretation between clay and sandstone makes no sense), but interpolation is authorized for continuous scalars. This implies that the calculations and the graphics representation of isosurfaces or isocontours will differ for continuous and discrete data. In 3D basin modeling, the simulation of the deposition of sedimentary bodies may need time-varying grids (e.g., the number of layers may depend on time). A specific grid management is then designed so that an animated visualization of the deposition process is available on the workstation process is available on the workstation screen. An interpolation in time is introduced for reservoir-simulation data to avoid having to store all simulation steps and to allow visualization of a smooth movement of fluid flow. Visualization of wells, cutting planes defined by two vertical wells, and successions of cutting planes defined by successions of interactively chosen wells are also among the specific needs encountered in the scientific fields for which our visualization software is designed. Data To Be Visualized Concept of Discrete and Continuous Data. We handle scalar data (lithofacies, pressure, saturation, etc.), not vector data. Data are computed on a grid that is described later. We distinguish two kinds of data: discrete and continuous. Discrete data are lithofacies values, and continuous data include such scalars as pressure, saturation, and porosity. Note that most general-purpose porosity. Note that most general-purpose visualization packages handle only continuous data, such as oil saturation, which may take an infinity of values within some authorized range (say between 0 and 1). Moreover, in such packages, it is implicitly assumed that the numerical values to be visualized are point samples of a continuous function point samples of a continuous function (continuous in space), which cannot be the case for lithofacies values. The set of lithofacies values the user deals with is finite, and there is no possible continuity. Lithofacies values actually are attributes rather than numerical values, although the simulation programs provide them to the visualization system as provide them to the visualization system as numerical values. Because discrete and continuous data are intrinsically different, their graphics representations do not have the same meaning. As a matter of fact, when continuous data are visualized with colors on a computer screen, each color represents a class of valuesnot just onebecause the number of available colors is finite. Even though the colored picture on the screen may look smooth, an infinite range of numerical values is approximated by a finite set of colors. On the contrary, the color representation for discrete values is not an approximation because there is an exact correspondence between a color and a value.

A subgridding method for the time-domain finite-difference method to solve Maxwell's equations

A modification to the time-domain finite-difference method (TDFDM) that uses a variable step size is investigated. The entire computational volume is divided into a coarse grid with a large step size. A fine grid with a small step size is introduced only around discontinuities. The corresponding time increments are related to the spatial increments with the same ratio in order to minimize the numerical dispersion. The fields within the coarse and fine grids are found using the TDFDM, while an interpolation in space and time is utilized to calculate the tangential electric field on the coarse-fine grid boundary. This subgridding decreases the required computer memory and therefore expands the capability of the TDFDM. The technique is shown to be numerically stable and does not entail any extra numerical error. The method is applied to the calculation of waveguides and microstrips.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Gas chromatographic—mass spectrometric analysis of tar compounds formed during pyrolysis of rice husks

Pyrolysis of agricultural waste to produce fuel gas involves formation of tars as noxious by-products. In this paper the qualitative analysis of tars formed during pyrolysis of rice husks is presented, based on identification by gas chromatography—mass spectrometry and interpolation of retention times on a polyaromatic hydrocarbon index scale. The influence of some reaction parameters on product formation is briefly discussed.

Instantaneous Cross-sectional Flow Velocity Profiles: A Comparative Study of Two Ultrasound Doppler Methods Applied to an In Vitro Pulsatile Flow Model

Two methods based on different techniques for construction of cross-sectional flow velocity profiles from Doppler ultrasound signals were compared: an intraluminal method using pulsed-wave Doppler echocardiography and an extraluminal method using two-dimensional (color) Doppler ultrasound. The methods were applied to an in vitro pulsatile flow model. With the intraluminal method, pulsed Doppler recordings obtained throughout several flow pulses at different positions across a tube were digitized, and cross-sectional flow velocity profiles were obtained by matching the onset of flow velocity at the various positions. With the extraluminal method, cross-sectional flow velocity profiles were obtained by time interpolation between the digital flow velocity data obtained from several flow velocity maps. The first flow velocity map was recorded at onset of flow and the following maps were incrementally delayed with 20 msec from one flow pulse to the next. The time lag caused by the time needed to update each of the flow velocity maps was compensated for by time interpolation between the sequentially recorded flow velocity maps. The cross-sectional flow velocity profiles obtained with the two methods were compared at identical positions within the tube model at equal flow settings and throughout the pulsatile flow periods. At three different flow settings with peak flow velocity of 0.3, 0.5, and 0.7 m/sec, the difference (mean +/- SD) between the obtained velocities were 0.01 +/- 0.04, -0.01 +/- 0.05, and -0.03 +/- 0.07 m/sec, respectively. The findings suggest that cross-sectional flow velocity profiles from pulsatile flow velocity recordings can be obtained equally well with both methods.

Advanced time‐domain formulation of BEM for two‐dimensional transient elastodynamics

AbstractIn this paper, a new formulation for two‐dimensional time‐domain transient elastodynamic analysis by the Boundary Element Method (BEM) is presented. The traction kernel is derived by using the causality of the waves and the resulting kernel is explicit and much simpler than the ones that have appeared in the recent literature. An appropriate set of linear time interpolation functions together with quadratic spatial variations are incorporated. Moreover, the algorithm has a capability of handling problems with multiply connected regions. All of these advanced features have resulted in an efficient formulation capable of producing very accurate results and represent significant improvements over the present level of sophistication in this area. This above algorithm is now a part of the general purpose BEM code known as GPBEST.

Boundary element method with high order time element for transient eddy current problems

A boundary-element method with a quadratic time interpolation technique is developed for transient eddy-current problems. A time-domain discretization element and its integral formulations are presented. Two examples are given and compared with previous solutions to demonstrate that the proposed technique has the important advantage that a larger time step can be used. >

A unified formulation of two existing time‐domain boundary‐element approaches

AbstractTwo apparently different time‐domain boundary‐element formulations for plane‐stress/plane‐strain elastodynamic problems exist in the literature. The present paper shows why one of the formulations, which is valid for a particular type of interpolation function, forms part of the other, which can be used with any interpolation function. The main differences presented in the past between the two existing time‐domain boundary‐element methods were based on an incorrect expression of the tractions in the complete plane due to the rectangular impulse load. Results obtained in the past which were presented to evaluate the differences between the two formulations are shown to be incorrect. A compact expression for the fundamental solution integrated along a time step when the time interpolation functions of all the boundary variables are assumed to be piecewise constant is presented. This integral gives the same tractions as those corresponding to a rectangular impulse load.

Cross sectional early mitral flow velocity profiles from colour Doppler.

Instantaneous cross sectional flow velocity profiles from early mitral flow in 10 healthy men were constructed by time interpolation of the velocity data from each point in sequentially delayed two dimensional digital Doppler ultrasound maps. This interpolation allows correction of the artificially produced skewness of velocities across the flow sector caused by the time taken to scan the flow sector for velocity recording of pulsatile blood flow. These results suggested that early mitral flow studied in an apical four chamber view is variably skewed both at the leaflet tips and at the annulus. The maximum flow velocity overestimated the cross sectional mean velocity at the same time by a factor of 1.2-2.2. Also the maximum time velocity integral overestimated the cross sectional mean time velocity integral to the same extent. This cross sectional skew must be taken into account when calculation of blood flow is based on recordings with pulsed wave Doppler ultrasound from a single sample volume.

Extrapolation and interpolation by time-scaling in systems with diffusion-controlled kinetics and first-order reaction rates.

The interpolation or extrapolation in time of physicochemical processes from experimental data is often difficult. A theoretically derived time-scaling procedure using an exposure variable of the concentration integrated in time, with at most one adjustable parameter was applied successfully to three systems taken from metallurgical, agricultural and environmental engineering. This scaling rule is potentially useful as a research or management tool for systems that are too complex for mechanistic modelling. (Abstract retrieved from CAB Abstracts by CABI’s permission)

Computation of dynamic stress intensity factors by the time domain boundary integral equation method-I. Analysis

Application of the direct time domain boundary integral equation method (BIEM) to the solution of a number of elastodynamic crack problems is presented. In this part I, we describe the analysis which includes the basic governing differential equations, their transformation to boundary integral equations and the numerical solution procedure of the discretized form of the BIE. In addition to the usual constant interpolation in space and time of tractions and displacements on the boundary, a new boundary element which incorporates quadratic variation in space and linear variation in time (of the traction and displacements) is developed. These two boundary elements are implemented in a computer code and are used in the examples described in part II. A consistent method of estimation of the dynamic stress intensity factors in conjunction with the two types of the elements mentioned is described. No special singular crack tip elements are used other than the quadratic isoparametric quarter-point boundary elements for modeling the crack tip singularities. Subsequent results show that the numerical solution is accurate and has good convergence properties with regard to mesh refinement and time step size.

On improved methods for timing the digitisation of AC waveforms

The NPL digital sampling AC wattmeters, which are used for calibration work, each require the generation of sample timing pulses suitably locked to the frequency of the AC which is to be measured. Repetitive waveforms representing the instantaneous test voltage and test current are digitised at equal intervals of time harmonically related to the period of the waveforms. A new NPL standard wattmeter calibrator (Mk III) incorporates improved sample timing generation. The Mk III uses a crystal digital oscillator to govern both the sample timing and the AC source frequency. This avoids reliance on timing interpolation uniformity within an input period; only digital frequency dividers are needed. Alternatively, commercial frequency synthesizers can be used, with a common master frequency, to give sampling and signal frequencies. Either alternative allows digital phase control, and reduces the use of special-purpose precision analogue electronics.