High Speed Dynamics of Collapsing Cylindrical Dust Fluid

We construct approximate solutions that will describe the last stage of cylindrically symmetric gravitational collapse of dust fluid. Just before the spacetime singularity formation, the speed of the dust fluid might be almost equal to the speed of light by gravitational acceleration. Therefore the analytic solution describing the dynamics of cylindrical null dust might be the crudest approximate solution of the last stage of the gravitational collapse. In this paper, we regard this null dust solution as a background and perform `high-speed approximation' to know the gravitational collapse of ordinary timelike dust fluid; the `deviation of the timelike 4-velocity vector field from null' is treated as a perturbation. In contrast with the null dust approximation, our approximation scheme can describe the generation of gravitational waves in the course of the cylindrically symmetric dust collapse.Comment: 15 page

Time-domain NIRS system based on supercontinuum light source and multi-wavelength detection: Validation for tissue oxygenation studies

We present and validate a multi-wavelength time-domain near-infrared spectroscopy (TD-NIRS) system that avoids switching wavelengths and instead exploits the full capability of a supercontinuum light source by emitting and acquiring signals for the whole chosen range of wavelengths. The system was designed for muscle and brain oxygenation monitoring in a clinical environment. A pulsed supercontinuum laser emits broadband light and each of two detection modules acquires the distributions of times of flight of photons (DTOFs) for 16 spectral channels (used width 12.5 nm / channel), providing a total of 32 DTOFs at up to 3 Hz. Two emitting fibers and two detection fiber bundles allow simultaneous measurements at two positions on the tissue or at two source-detector separations. Three established protocols (BIP, MEDPHOT, and nEUROPt) were used to quantitatively assess the system's performance, including linearity, coupling, accuracy, and depth sensitivity. Measurements were performed on 32 homogeneous phantoms and two inhomogeneous phantoms (solid and liquid). Furthermore, measurements on two blood-lipid phantoms with a varied amount of blood and Intralipid provide the strongest validation for accurate tissue oximetry. The retrieved hemoglobin concentrations and oxygen saturation match well with the reference values that were obtained using a commercially available NIRS system (OxiplexTS) and a blood gas analyzer (ABL90 FLEX), except a discrepancy occurs for the lowest amount of Intralipid. In-vivo measurements on the forearm of three healthy volunteers during arterial (250 mmHg) and venous (60 mmHg) cuff occlusions provide an example of tissue monitoring during the expected hemodynamic changes that follow previously well-described physiologies. All results, including quantitative parameters, can be compared to other systems that report similar tests. Overall, the presented TD-NIRS system has an exemplary performance evaluated with state-of-the-art performance assessment methods

Numerical Approaches to Spacetime Singularities

This Living Review updates a previous version which its itself an update of a review article. Numerical exploration of the properties of singularities could, in principle, yield detailed understanding of their nature in physically realistic cases. Examples of numerical investigations into the formation of naked singularities, critical behavior in collapse, passage through the Cauchy horizon, chaos of the Mixmaster singularity, and singularities in spatially inhomogeneous cosmologies are discussed.Comment: 51 pages, 6 figures may be found in online version: Living Rev. Relativity 2002-1 at www.livingreviews.or

Observations With Regard To Massively Parallel Computation For Monte Carlo Simulation Of Stochastic Dynamical Systems

The evolution of stochastic dynamical systems is governed by Fokker--Planck equations if the response process is Markovian. Analytical solutions for the transient response of multidimensional systems exist only for the simplest dynamical systems. The evolution of the transition probability density function over the phase space has been solved numerically for various low dimensional systems subjected to additive and multiplicative white noise excitations using the finite element method. Systems of higher order, however, pose difficulty when using standard finite element formulations due to memory requirements and computational expense. Direct Monte Carlo simulation (MCS), while often regarded as less elegant than other methods, can be used to solve problems of significantly higher complexity. The number of realizations required to accurately produce the transition probability density function over the entire phase space, especially in the tails, is large, but since each realization is e..

Depth-resolved assessment of changes in concentration of chromophores using time-resolved near-infrared spectroscopy: estimation of cytochrome-c-oxidase uncertainty by Monte Carlo simulations

Time-resolved near-infrared spectroscopy (TR-NIRS) measurements can be used to recover changes in concentrations of tissue constituents (ΔC) by applying the moments method and the Beer-Lambert law. In this work we carried out the error propagation analysis allowing to calculate the standard deviations of uncertainty in estimation of the ΔC. Here, we show the process of choosing wavelengths for the evaluation of hemodynamic (oxy-, deoxyhemoglobin) and metabolic (cytochrome-c-oxidase (CCO)) responses within the brain tissue as measured with an in-house developed TR-NIRS multi-wavelength system, which measures at 16 consecutive wavelengths separated by 12.5 nm and placed between 650 and 950 nm. Data generated with Monte Carlo simulations on three-layered model (scalp, skull, brain) for wavelengths range from 650 to 950 nm were used to carry out the error propagation analysis for varying choices of wavelengths. For a detector with a spectrally uniform responsivity, the minimal standard deviation of the estimated changes in CCO within the brain layer, σ∆CbrainCCO = 0.40 µM, was observed for the 16 consecutive wavelengths from 725 to 912.5 nm. For realistic a detector model, i.e. the spectral responsivity characteristic is considered, the minimum, σ∆CbrainCCO = 0.47 µM, was observed at the 16 consecutive wavelengths from 688 to 875 nm. We introduce the method of applying the error propagation analysis to data as measured with spectral TR-NIRS systems to calculate uncertainty of recovery of tissue constituents concentrations

Time-domain NIRS system based on supercontinuum light source and multi-wavelength detection: Validation for tissue oxygenation studies

We present and validate a multi-wavelength time-domain near-infrared spectroscopy (TD-NIRS) system that avoids switching wavelengths and instead exploits the full capability of a supercontinuum light source by emitting and acquiring signals for the whole chosen range of wavelengths. The system was designed for muscle and brain oxygenation monitoring in a clinical environment. A pulsed supercontinuum laser emits broadband light and each of two detection modules acquires the distributions of times of flight of photons (DTOFs) for 16 spectral channels (used width 12.5 nm / channel), providing a total of 32 DTOFs at up to 3 Hz. Two emitting fibers and two detection fiber bundles allow simultaneous measurements at two positions on the tissue or at two source-detector separations. Three established protocols (BIP, MEDPHOT, and nEUROPt) were used to quantitatively assess the system's performance, including linearity, coupling, accuracy, and depth sensitivity. Measurements were performed on 32 homogeneous phantoms and two inhomogeneous phantoms (solid and liquid). Furthermore, measurements on two blood-lipid phantoms with a varied amount of blood and Intralipid provide the strongest validation for accurate tissue oximetry. The retrieved hemoglobin concentrations and oxygen saturation match well with the reference values that were obtained using a commercially available NIRS system (OxiplexTS) and a blood gas analyzer (ABL90 FLEX), except a discrepancy occurs for the lowest amount of Intralipid. In-vivo measurements on the forearm of three healthy volunteers during arterial (250 mmHg) and venous (60 mmHg) cuff occlusions provide an example of tissue monitoring during the expected hemodynamic changes that follow previously well-described physiologies. All results, including quantitative parameters, can be compared to other systems that report similar tests. Overall, the presented TD-NIRS system has an exemplary performance evaluated with state-of-the-art performance assessment methods

Recipes for diffuse correlation spectroscopy instrument design using commonly utilized hardware based on targets for signal-to-noise ratio and precision

Over the recent years, a typical implementation of diffuse correlation spectroscopy (DCS) instrumentation has been adapted widely. However, there are no detailed and accepted recipes for designing such instrumentation to meet pre-defined signal-to-noise ratio (SNR) and precision targets. These require specific attention due to the subtleties of the DCS signals. Here, DCS experiments have been performed using liquid tissue simulating phantoms to study the effect of the detected photon count-rate, the number of parallel detection channels and the measurement duration on the precision and SNR to suggest scaling relations to be utilized for device design