Fluid Sphere Model Research Articles

Isotropic Durgapal IV fluid sphere in bigravity

We analyze an isotropic uncharged fluid sphere model within bigravity considering the Durgapal IV metric (M.C. Durgapal, J. Phys. A: Math. Gen. 15, 2637 (1982)). In this work, we investigate the effects of the scale parameter k on the local matter distribution. Here, we have chosen the compact star candidate SMC X-1 with observed values of mass = (1.29 ± 0.05) M⊙ and radius [Formula: see text] km, respectively, to analyze our results analytically as well as graphically. For smaller values of k, we get the stiff (or hard) equation of state (EoS). Here, we solve the modified Einstein field equations in the presence of the background metric γμν. Due to this constant curvature background, the density and pressure terms are modified by adding an extra term, which affects the EoS. For r ≪ k, the background de Sitter space–time reduces into Minkowski form, and the coupling vanishes. We discuss certain physical quantities of our obtained solution, such as density, isotropic pressure, sound speed, pressure-density gradients, compactness, and surface redshift, to claim the physical viability of our model. It is found that our model clearly satisfies all the energy conditions, the causality condition, and the dynamical equilibrium via a modified Tolman–Oppenheimer–Volkov equation. Finally, we can conclude that our proposed model is physically realistic and well behaved.

Static Weyssenhoff Fluid Sphere Models in Einstein–Cartan Theory of Gravitation

Static Weyssenhoff Fluid Sphere Models in Einstein–Cartan Theory of Gravitation

Stellar model for anisotropic compact stars in Schwarzchild’s coordinates

In this article, we have presented a completely new, well-behaved, physically acceptable and stable anisotropic fluid sphere model. For this purpose we have used a well-known Vaidya-Tikekar [J. Astrophys. Astron. 3, 325 (1982)] ansatz for metric potential ${g}_{rr}$ to generate the model. We have investigated the various physical aspects for our model such as energy density, pressure (radial as well as transverse), anisotropy factor, mass, compactness parameter, surface, and gravitational redshifts. Energy conditions, equilibrium, and stability analysis has been done using graphs. This ensured that our proposed solutions are well-behaved and hence represent physically acceptable models for anisotropic fluid spheres. For comparison with observational data we have considered the compact stars: Her X-1, $4\mathrm{U}1538\penalty1000-\hskip0pt52$, SAX $\mathrm{J}1808.4\penalty1000-\hskip0pt3658$, LMC X-4, SMC X-1, EXO $1785\penalty1000-\hskip0pt248$, Cen X-3, 4U $1820\penalty1000-\hskip0pt30$, PSR $\mathrm{J}1903+327$, 4U $1608\penalty1000-\hskip0pt52$, Vela X-1, PSR $\mathrm{J}1614\penalty1000-\hskip0pt2230$, Cyg X-2 and PSR $\mathrm{B}1913+16$. The calculated value of central density of each of these compact stars, using this model, is of order ${10}^{14}$ or ${10}^{15}$, which is considerably high and consistent with ultracompact stars. We have also estimated the approximate moment of inertia for each of the considered compact stars.

A generalized anisotropic model for super dense stars

A static anisotropic relativistic fluid sphere model with regular geometry and finite hydrostatic functions is presented. In the interior of the sphere, the density, radial pressure and tangential pressure are positives, monotonically decreasing with increasing radius and the radial pressure vanishes at the surface of the matter distribution and is joined continuously to the exterior Schwarzschild’s solution at this surface. The speeds of the radial and tangential sound are positive and lower than the speed of light, that is, the causal condition is not violated, and also the behavior of these guarantees that the model is potentially stable. Furthermore, the range of the compactness ratio is characteristic of compact stars and it is shown that the effect of the anisotropy generates that the speed of the radial sound can behave as a function monotonically increasing or monotonically decreasing.

Weyssenhoff fluid sphere models in Einstein–Cartan theory

We obtain three models for geodesic flows and three models for non-geodesic flows of Weyssenhoff fluid considering it as the source of gravitation and spin in the Einstein–Cartan field equations. Influence of spin on the pressure, density, equation of state, and the kinematical parameters is observed in both geodesic and non-geodesic models.

Optimization of Ultrasound Backscatter Spectroscopy to Assess Neurotoxic Effects of Anesthesia in the Newborn Non-human Primate Brain

Studies in animal models have revealed that long exposures to anesthetics can induce apoptosis in the newborn and young developing brain. These effects have not been confirmed in humans because of the lack of a non-invasive, practical in vivo imaging tool with the ability to detect these changes. Following the successful use of ultrasound backscatter spectroscopy (UBS) to monitor in vivo cell death in breast tumors, we aimed to use UBS to assess the neurotoxicity of the anesthetic sevoflurane (SEVO) in a non-human primate (NHP) model. Sixteen 2- to 7-day-old rhesus macaques were exposed for 5 h to SEVO. Ultrasound scanning was done with a phased array transducer on a clinical ultrasound scanner operated at 10 MHz. Data consisting of 10–15 frames of radiofrequency (RF) echo signals from coronal views of the thalamus were obtained 0.5 and 6.0 h after initiating exposure. The UBS parameter “effective scatterer size" (ESS) was estimated by fitting a scattering form factor (FF) model to the FF measured from RF echo signals. The approach involved analyzing the frequency dependence of the measured FF to characterize scattering sources and selecting the FF model based on a χ2 goodness-of-fit criterion. To assess data quality, a rigorous acceptance criterion based on the analysis of prevalence of diffuse scattering (an assumption in the estimation of ESS) was established. ESS changes after exposure to SEVO were compared with changes in a control group of five primates for which ultrasound data were acquired at 0 and 10 min (no apoptosis expected). Over the entire data set, the average measured FF at 0.5 and 6.0 h monotonically decreased with frequency, justifying fitting a single FF over the analysis bandwidth. χ2 values of a (inhomogeneous continuum) Gaussian FF model were one-fifth those of the discrete fluid sphere model, suggesting that a continuum scatterer model better represents ultrasound scattering in the young rhesus brain. After application of the data quality criterion, only 5 of 16 subjects from the apoptotic group and 5 of 5 subjects from the control group fulfilled the acceptance criteria. All subjects in the apoptotic group that passed the acceptance criterion exhibited a significant ESS reduction at 6.0 h. These changes (–6.4%, 95% Interquartile Range: –14.3% to –3.3%) were larger than those in the control group (–0.8%, 95% Interquartile Range: –2.0% to 1.5%]). Data with a low prevalence of diffuse scattering corresponded to possibly biased results. Thus, ESS has the potential to detect changes in brain microstructure related to anesthesia-induced apoptosis.

High-Frequency Quantitative Ultrasound Spectroscopy of Excised Canine Livers and Mouse Tumors Using the Structure Factor Model.

Three scattering models were examined for characterizing ex vivo canine livers and HT29 mouse tumors in the 10-38- and the 15-42-MHz frequency bandwidth, respectively. The spherical Gaussian model (SGM) and the fluid sphere model (FSM) that were examined are suitable for dealing with sparse media, whereas the structure factor model (SFM) is adapted for characterizing concentrated media. For the canine livers, the scatterer radius and the acoustic concentration estimated with the three models were similar and matched well the nuclear structures obtained from histological analysis (with relative errors less than 7%). These results show that the livers could be considered as a diluted medium and that the nuclei in liver could be a dominant source of scattering. For the homogeneous mouse tumors, containing mostly viable HT29 cells, scatterer radius and volume fraction estimated with the SFM showed good agreement with the whole cell structures obtained from histological analysis (with relative errors less than 15%), whereas the sparse models (the SGM and the FSM) gave no consistent quantitative ultrasound parameters. This suggests that the viable HT29 cell areas have densely packed cellular content and that the whole HT29 cell could be responsible for scattering. For the heterogeneous tumors, the hyperechogenic zones observed in the B-mode images were linked to the presence of small necrotic areas surrounded by viable HT29 cells. Comparison between sparse and concentrated models shows that these hyperechogenic zones could be considered as a concentrated medium.

In Vivo Estimation of Attenuation and Backscatter Coefficients From Human Thyroids.

Fine-needle aspiration (FNA) remains the gold standard for the diagnosis of thyroid cancer. However, currently, a large number of FNA biopsies result in negative or undetermined diagnosis, which suggests that better noninvasive tools are needed for the clinical management of thyroid cancer. Spectral-based quantitative ultrasound (QUS) characterizations may offer a better diagnostic management as previously demonstrated in mouse cancer models ex vivo. As a first step toward understanding the potential of QUS markers for thyroid disease management, this paper deals with the spectral-based QUS estimation of healthy human thyroids in vivo. Twenty volunteers were inspected by a trained radiologist using two ultrasonic imaging systems, which allowed them to acquire radio-frequency data spanning the 3-16-MHz frequency range. Estimates of attenuation coefficient slope (ACS) using the spectral logarithmic difference method had an average value of [Formula: see text]) with a standard deviation of [Formula: see text]. Estimates of backscatter coefficient (BSC) using the reference-phantom method had an average value of [Formula: see text] over the useful frequency range. The intersubject variability when estimating BSCs was less than 1.5dB over the analysis frequency range. Further, the effectiveness of three scattering models (i.e., fluid sphere, Gaussian, and exponential form factors) when fitting the experimentally estimated BSCs was assessed. The exponential form factor was found to provide the best overall goodness of fit ( R2 = 0.917), followed by the Gaussian ( R2 = 0.807) and the fluid-sphere models ( R2 = 0.752). For all scattering models used in this study, average estimates of the effective scatterer diameter were between 44 and 56 μm. Overall, an excellent agreement in the estimated attenuation and BSCs with both scanners was exhibited.

Effects of cell spatial organization and size distribution on ultrasound backscattering

In ultrasound tissue characterization dealing with cellular aggregates (such as tumors), it can be hypothesized that cell microstructure and spatial distribution dominate the backscatter signal. Effects of spatial organization and size distribution of nuclei in cell aggregates on ultrasound backscatter are examined in this work using 2-D computer simulations. The nuclei embedded in cytoplasm were assumed to be weak scatterers of incident ultrasound waves, and therefore multiple scattering could be neglected. The fluid sphere model was employed to obtain the scattering amplitude for each nucleus and the backscatter echo was generated by summing scattered signals originating from many nuclei. A Monte Carlo algorithm was implemented to generate realizations of cell aggregates. It was found that the integrated backscattering coefficient (IBSC) computed between 10 and 30 MHz increased by about 27 dB for a spatially random distribution of mono-disperse nuclei (radius = 4.5 μm) compared with that of a sample of periodically positioned mono-disperse nuclei. The IBSC also increased by nearly 7 dB (between 10 and 30 MHz) for a spatially random distribution of poly-disperse nuclei (mean radius ± SD = 4.5 ± 1.54 μm) compared with that of a spatially random distribution of mono-disperse nuclei. Two different Gaussian pulses with center frequencies 5 and 25 MHz were employed to study the backscatter envelope statistics. An 80% bandwidth was chosen for each case with approximately 0.32 mm as the full-width at half-maximum (FWHM) for the first pulse and 0.06 mm for the second. The incident beam was approximated as a Gaussian beam (FWHM = 2.11 and 1.05 mm for those pulses, respectively). The backscatter signal envelope histograms generally followed the Rayleigh distribution for mono-disperse and poly-disperse samples. However, for samples with partially ordered nuclei, if the irradiating pulse contained a frequency for which ultrasound wavelength and scatter periodicity became comparable (d ~ λ/2), then the histograms were better fitted by the Nakagami distribution. This study suggests that the shape of an envelope histogram depends upon the periodicity in the spatial organization of scatterers and bandwidth of the ultrasound pulse.

음향자원조사를 위한 동물플랑크톤 요각류의 음향산란이론모델의 검토

Several theoretical acoustic scattering models were applied to estimate the target strength (TS) for assessing the biomass of zooplankton, to overcome the difficulty of direct measurements. Acoustical scattering characteristics of copepods were estimated using three theoretical models, and the application of the models was evaluated for four frequencies of a scientific echo sounder. The scattering directivity by the body shapes of copepods at 200 kHz and 420 kHz was significantly affected by TS patterns. Averaged TS, however, were similar at higher frequencies. Consequently, a low frequency model, such as a truncated fluid sphere model, provides a good acoustical biomass estimation. The regressions of TS and 30 logL were < <TEX>$TS_{200\;kHz}$</TEX> >= 30logL-118.4 (<TEX>$R^2=0.716$</TEX>) and < <TEX>$TS_{420 kHz}$</TEX> > =30 logL-108.8 (<TEX>$R^2=0.758$</TEX>), respectively.

The measurement of ultrasound scattering from individual micron-sized objects and its application in single cell scattering

The measurement of the ultrasound backscatter from individual micron-sized objects such as cells is required for various applications such as tissue characterization. However, performing such a measurement remains a challenge. For example, the presence of air bubbles in a suspension of cells during the measurements may lead to the incorrect interpretation of the acoustic signals. This work introduces a technique for measuring the ultrasound backscatter from individual micron-sized objects by combining a microinjection system with a co-registered optical microscope and an ultrasound imaging device. This allowed the measurement of the ultrasound backscatter response from a single object under optical microscope guidance. The optical and ultrasonic data were used to determine the size of the object and to deduce its backscatter responses, respectively. In order to calibrate the system, the backscatter frequency responses from polystyrene microspheres were measured and compared to theoretical predictions. A very good agreement was found between the measured backscatter responses of individual microspheres and theoretical predictions of an elastic sphere. The backscatter responses from single OCI-AML-5 cells were also investigated. It was found that the backscatter responses from AML cells are best modeled using the fluid sphere model. The advantages, limitations, and future applications of the developed technique are discussed.

AN ALTERNATIVE PROPOSAL: ACOUSTIC TECHNIQUES TO ASSES DETECTION AND MONITORING OF TOXIC ALGAL BLOOMS

An alternative methodology consisting in the application of acoustic techniques to asses detection and monitoring of toxic algal blooms is presented here. Successive steps in this direction led to already reported results [Blanc et al., 2000] achieved under the frame of a multidisciplinary research programme conducted in the Argentinean Naval Service of Research and Development. First efforts were focused in the examination of the acoustical scattering behaviour of single-species cultures of Skeletonema costatum. For this purpose a pulse-echo electronic equipment was developed, including home-made piezoelectric transducers with an operating frequency centred at 2.6 MHz. A slight modified Johnson's fluid-sphere model was used. Numerical Abundance estimates from at-lab acoustic determinations of Volume Backscattering Strengths were obtained. When they were compared with predicted values computed through the adopted model and traditional optical counting, satisfactory results were obtained. More recently, single cultures of dinoflagellates, namely, Gymnodinium sp., were selected to enable a further stage of acoustic laboratory measurements. Controlled observations of its optimum growth conditions along a six-months period have been performed. The effects of different patterns of light and temperature have been analysed. Simultaneous work on modifying existing models of Backscattering Cross-Sections to provide a realistic description of dinoflagellates physical properties is being performed

Impulse scattering processes of an elastic sphere

The ‘‘movable rigid sphere’’ scattering model of Hickling and Wang [J. Acoust. Soc. Am. 39, 276–279 (1966)] incorporates the translational ‘‘rebound’’ response of the scatterer to the incident field. However, as a physically unrealizable object, the rigid sphere has limited applicability. Recently, it was shown [J. Acoust. Soc. Am. 106, 553–564 (1999)] that both the movable rigid sphere and Anderson’s fluid sphere model [J. Acoust. Soc. Am. 22, 426–431 (1950)] are limiting cases of Faran’s elastic sphere scattering theory [J. Acoust. Soc. Am. 23, 405–418 (1951)]. In this paper, the time domain impulse response is used to demonstrate the three dimensional scattering of an elastic sphere and its special cases. The critical factor is the shear rigidity modulus. For normal elastic values of the modulus, shear waves dominate the scattering response. When the rigidity is high, the shear waves travel more rapidly through the sphere, and its motion becomes increasingly characterized as a rebound translation without change of shape. Wave conversion at the boundary is also inhibited. For low or vanishing rigidity, only compressional waves are supported, and these determine the scattering response. The presentation will be illustrated by movie animations. [Work supported by ONR.]

Multistatic, multifrequency scattering from zooplankton

Very satisfactory results have been obtained in estimating size abundances of small zooplankton such as copepods from inversion of multifrequency backscattering measurements. Application of this method has become almost routine in many situations. Fluctuations in the scatterer physical properties (density and compressibility) tend principally to cause errors in the abundance estimates whereas size estimates are largely unaffected. The model commonly employed for small crustacean scatterers, a truncated-mode version of the Anderson fluid sphere model, predicts bistatic scattering as well as monostatic backscattering. The behavior of bistatic scattering at angles approaching 90 deg predicted by this model shows that scattering spectra at these angles are quite sensitive to physical properties. This suggests that simultaneous measurements at multiple frequencies and one or more off-axis angles might permit estimation of the physical properties of zooplanktonic scatterers as well as their sizes. Preliminary modeling has been done for a single fluid scatterer to illustrate the potential for simultaneous estimation of size, density, and compressibility of zooplanktonic organisms in a laboratory setting. The character of the bistatic scattering may argue for nontraditional methods for inverting this sort of data.

Target strengths of Antarctic krill (E u p h a u s i a s u p e r b a) at 38 and 120 kHz

Encaged aggregations of live krill in good to pristine condition have been ensonified at 38 and 120 kHz. Concurrent underwater television observations of behavior resemble those made by underwater divers in naturally occurring swarms, with comparably high densities of the order of 104 animals/m3 . Mean, single-animal target strengths have been inferred from measurements of echo energy. For aggregations with mean lengths in the range [30,39] mm, the mean single-krill target strengths are in the range [−88,−83] dB at 38 kHz and [−81,−74] dB at 120 kHz. Collateral measurements on some of the same encaged specimens determined a density contrast of 1.0357±0.0067 and sound-speed contrast of 1.0279±0.0024, relative to seawater. These numbers have been used with the fluid-sphere model as stated by Greenlaw [Limnol. Oceanogr. 24, 226–242 (1979)] . Computed backscattering cross sections have been averaged over the length distributions of each measured aggregation, resulting in target strength predictions in the range [−86,−80] dB at 38 kHz and [−79,−76] dB at 120 kHz.

Acoustic estimation of size distribution and abundance of zooplankton

A series of investigations were undertaken to observe and describe the sound backscattering process from larger zooplankton (euphausiids). The target strength versus frequency, size, and aspect angle of the organism was measured. The target strength is highly dependent on the density and sound speed contrasts between the target and the medium, and both these parameters were measured. From the target strength observations it was concluded that the fluid sphere model was insufficient as a scattering model for krill. Observations of the tilt angle distribution of krill at natural field conditions showed that they were distributed over a large region of tilt angles. The deficiencies of the fluid sphere models required the development of a new scattering model based on experimental data. This model predicts a decreasing target strength versus frequency in the geometric scattering region. The backscattering spectra of euphausiids were better described by our empirical model than by the fluid sphere models. Applying the empirical model to estimate size distribution and biomass of krill, we found strong correlation between the acoustically estimated distributions and those from net catches.

A simple model for the acoustic cross section of sand grains

Previous work on determining the acoustic cross section of sand grains [Geophys. Res. Lett. 9(2), 175–178 (1982)] identified a problem with the application of the simple compressible sphere model for the cross section. Use of the complete elastic sphere model [J. Acoust. Soc. Am. 34, 1582–1592 (1962)] failed to remove the conflict with observation. Application of the bistatic cross-section theorem to the angle averaged cross section shows that the appropriate cross section is the total absorption cross section, not the backscatter cross section. The total absorption cross section for the fluid sphere model is found to be in semiquantitative agreement with scattering data for sand grains.

Sound scattering from a fluid sphere revisited

The backscattering frequency responses for euphausiids and copepods are predicted using a fluid-sphere model and measured physical properties for the zooplankters. The fluid-sphere model is also compared with the resonant gas bubble equation.

High-frequency backscattering from marine zooplankton

It is often assumed that backscattering from marine zooplankton may be satisfactorily estimated from the Rayleigh fluid-sphere scattering model at frequencies such that ka &amp;lt; 1. At higher frequencies the fluid sphere model of Anderson [J. Acoust. Soc. Am. 22, 426–43 (1950)] has been thought approximately valid at least for the more spherical plankton. A series of acoustical and physical measurements was made on preserved specimens of three common zooplankters (a copepod, Calanus marshallae; an euphausiid, Euphausia pacifica; and a penaeid shrimp, Sergestes similis Hansen). Target strengths of individual specimens were measured in a freshwater tank at eight frequencies between 220 and 1100 kHz. Densities, compressional wave sound speeds, and displacement volumes of the samples were measured to enable calculation of predicted target strengths from the Anderson model. Measured target strengths of the copepod agreed with predictions up to ka = 1, but were increasingly higher than predicted up to the highest ka obtained (ka ∼ 4). The euphasusiid and sergestid were found to highly directional scatterers; anterior aspect target strengths were 10–20 dB lower than side or dorsal aspect values. Surprisingly, the general levels and gross structure of the side/dorsal aspect target strengths were in reasonable agreement with the Anderson model up to ka ∼ 11 (euphausiid) and ka ∼ 7 (sergestid). Data in the range ka ⩽ 1 could not be obtained for these plankters because of equipment problems. [Supported by ONR.]

Sound scattering from a fluid sphere revisited

The fluid sphere model is compared with scattering models for a free gas bubble in water and for the gas-filled swimbladder of a fish. The parameters discussed are frequency response and resonant frequency. The fluid sphere model is also used to predict scattering from euphausiids and copepods.