Prolate Ellipsoid Research Articles

Determination of sources of error and improvement in accuracy of left ventricular mass measurement by echocardiography.

Abnormal Left ventricular mass (LVM) prognosticates adverse cardiovascular events. Conventionally, LVM measured by echo assumes a prolate ellipsoid (PE) shape; however, it poorly correlates with reference standard of cardiac magnetic resonance imaging (CMR) derived LVM. PE model assumes LVL = 2 × LVID. We developed a new echo LVM formula based on LV length and tested for accuracy against CMR. A retrospective study of consecutive patients with an echocardiogram and CMR within 3months. Derivation (n = 170) and validation cohorts (n = 54) were used to test the new formula. Following analysis of correlation of interventricular septum (IVS), LV internal dimension (LVID), posterior wall (PW) and LVL between echo and CMR, a novel paraboloid-shape linear regression (PLR) model was derived. LVM by both models were compared to CMR. Poor correlation observed between actual and assumed LVL (0.52 with CMR; 0.44 with echo). Strong correlation was noted between echo and CMR measured LVL, LVID, IVS (r > 0.80) and a moderate correlation with PW (r = 0.62). Strong correlation of LVL was harnessed to develop PLR model, which significantly decreased paired error in derivation cohort (from 64 ± 42 to 22 ± 21 gm) and validation cohort (from 63 ± 46 to 25 ± 18 gm). Furthermore, it demonstrates significant reduction in absolute, relative errors and variability along with superior correlation in both cohorts. Between echo and CMR, LVL demonstrates one of the best correlation among LV dimensions. The assumption, LVL = 2 × LVID appears inaccurate. PLR model incorporates LVL and significantly improves accuracy, reduces variability of LVM.

Particle Scale Investigation of Influencing Factors on Heat Transfer in Nonspherical Particle–Fluid System

Abstract Heat transfer characteristics of random suspensions of 0.25 aspect ratio (AR) cylinders are investigated for Reynolds numbers (Re) between 10 and 300 and solid fraction (φ) ranging from 0.1 to 0.3 using particle resolved simulations. The effect of particle inclination with respect to flow and particle clustering on heat transfer is investigated. The Nusselt number decreases with an increase in inclination angle and the dependence becomes stronger as φ and Re increase. On the other hand, while prolate ellipsoid suspensions of AR 2.5 follow the same trend, the Nusselt number increases with inclination angle as AR increases to 5 and 10 and as φ increases. Local particle clustering nominally decreases the Nusselt number because of the dominance of thermal wakes. At low φ, this effect is felt only at low Re, but as φ increases, the effect spreads to higher Re. Similar but weaker trends are also found in suspensions of prolate ellipsoids of AR 2.5, 5, and 10. High AR, low Re prolate ellipsoids exhibit the greatest dependence of Nusselt number on local solid fraction. Implementation of two independent definitions of reference length, i.e., volume equivalent sphere diameter deq for ellipsoids and diameter dp of the cylindrical particle in the correlation of Tavassoli et al. (2015, “Direct Numerical Simulation of Fluid-Particle Heat Transfer in Fixed Random Arrays of Non-Spherical Particles,” Chem. Eng. Sci., 129, pp. 42–48) provides good estimates of the respective suspension mean Nusselt numbers.

Drag and heat transfer coefficients for axisymmetric nonspherical particles: A LBM study

In this work, the thermal lattice Boltzmann method with immersed moving boundary conditions has been employed to calculate the drag coefficients and Nusselt numbers for isolated axisymmetric nonspherical particles in uniform flow for a wide range of Reynolds numbers (Re) and aspect ratios (Ar). The simulation results demonstrate that the drag coefficient for ellipsoids and a spherocylinder evolves as sin2θ, viz. θ being the incident angle of the particle. However, the Nusselt number for prolate ellipsoids evolves as sinmθ, viz. m being a function of particle aspect ratio. A correlation for m has been developed for 1<Ar≤4 based on the simulation data. The Nusselt number for a spherocylinder of aspect ratio 4 evolves as sin1.278θ. Moreover, we observe that the drag coefficients and Nusselt numbers for a prolate ellipsoid of aspect ratio 4 and a spherocylinder of aspect ratio 4 are comparable with a maximal relative deviation 5%. Based on the simulation data and the data from literature, a drag correlation for oblate (0.2≤Ar<1 and 1≤Re≤100) and prolate (1≤Ar≤5 and 1≤Re≤2000) ellipsoids has been developed to broaden the range of applicability of existing drag correlations. The average relative deviation between the drag correlation and the fitting data is 9.4%. The Nusselt number correlation for prolate ellipsoids is valid for 1≤Ar≤4 and Re≤500. On the other hand, the Nusselt number correlation proposed for a spherocylinder is valid for Ar=4 and Re≤500. The new drag and Nusselt number correlations are expected to improve the accuracy of Euler-Lagrangian simulations of non-isothermal particulate flows comprising ellipsoids or spherocylinders.

Effect of particle shape on bedload sediment transport in case of small particle loading

The paper presents four direct numerical simulations of an open channel flow with geometrically resolved particles heavier than the fluid. In each simulation the same number of mono-disperse particles is considered, with the shape of the particles varied between the simulations, while conserving the volume. Three simulations are reported with non-spherical particles, here prolate ellipsoid, oblate ellipsoid, and Zingg-ellipsoid, and compared to a fourth one with spherical particles. The influence of the particle shape on the average fluid motion and on the disperse particle phase is investigated in the regime of low particle loading. It is found that the Reynolds stresses with spherical particles are much smaller compared to those with non-spherical particles. Of these, they are maximum in the case of oblate particles. Furthermore, the oblate spheroids are prominently found in the near-wall region and hardly roll. This behavior differs markedly from the behavior of the spherical particles, which preferably bounce and roll. The other two cases, with prolate ellipsoids and Zingg-ellipsoid behave between the two extreme cases of spherical and oblate particles. The oblate spheroids orient such that their symmetry axis is parallel to the wall-normal direction, whereas the prolate spheroids orient with their symmetry axis parallel to the streamwise direction. The Zingg-ellipsoids orient with their longest axis parallel to the streamwise direction and their smallest axis parallel to the wall-normal direction. This preferred orientation is more dominant in the near wall region. All effects mentioned are supported by quantitative evaluation of statistics and can serve as reference for future validations.

An approximation of geodesic circle passing through three points on an ellipsoid

Abstract In this paper we present an approximation method for a geodesic circle passing through three points on an oblate ellipsoid. Our method uses a prolate ellipsoid passing through the three points, and the new approximation curve is the intersection of the oblate and prolate ellipsoids, which can be obtained algebraically without iterations. The advantage of our approximation method is that it yields a significantly smaller approximation error. Compared to the plane section curve passing through the three points on the oblate ellipse, our method reduces the approximation error by at least 98 % 98\hspace{0.1667em}\% when the radii of geodesic circles are 100 km∼1000 km on the surface of the Earth. We illustrate the results using numerical examples.

Comparison of Spleen Volumes Estimated Using Planimetry and Prolate Ellipsoid Methods on MRI in Myelofibrosis Patients

Background: Splenomegaly is one of the most characteristic features of myelofibrosis (MF) with significant impact on the quality of life of patients. About 10% of MF patients present with severely symptomatic splenomegaly at diagnosis; another 50% develop it within 4 years of diagnosis. Pharmaceutical drug trials aimed at treating myelofibrosis have assessment of spleen size as one of its key trial endpoints. While assessment of spleen size (volume) by palpation is routinely performed in the clinic, unfortunately, it is not a precise and reliable method, a key requirement in drug trials. Medical imaging methods such as magnetic resonance imaging (MRI) and computed tomography (CT) provide a non-invasive approach to assessment of spleen volume. Both modalities allow acquisition of cross sectional abdominal images and enable full anatomical coverage of the spleen. Due to radiation concerns, MRI is preferred over CT modality. There are two approaches for analyzing cross sectional images for estimation of spleen volume - the planimetry method, that involves delineating spleen contours on each spleen slice to estimate complete spleen volume and the prolate ellipsoid method, that approximates the spleen to an ellipsoid structure and estimates spleen volume by using the prolate ellipsoid method (described below). The prolate method is a simple and quick way to assess spleen size compared to the planimetry method. However, the former method provides an approximate estimate of spleen size. The goal of this study was to compare the prolate method with planimetry method for estimating spleen volume for use in pharmaceutical clinical trials.Methods: A retrospective assessment of spleen volume in N=30 subjects with confirmed diagnosis of myelofibrosis was performed. All measurements were performed on T2 weighted MR images (5mm slice thickness/0.0 gap), acquired on MRI scanners from different manufacturers. All images were assessed for image quality prior to including them in the analysis and images without any images quality issues were included in this study. The analysis methods and calculation used for estimating spleen volume were as below:•Planimetry: Volume = ∑ [(Region of interest outlining the spleen boundary per slice) x (Slice thickness)].•Prolate Ellipsoid: Volume = 0.52 x (Longest diameter of the spleen) x (longest perpendicular diameter on the same trans-axial slice) x (vertical distance between the most superior and most inferior margins of the spleen)Results: Spleen volume estimated by planimetry and prolate method was 2113cc±1612cc and 2186cc±1538cc (mean ± Standard Deviation [S.D.]). The range of planimetry spleen volumes in this study was 210 to 5750cc. A plot of spleen volumes estimated using planimetry and prolate method showed high correlation (R2 = 0.97) between the two methods, however, the volume variation tends to increase for large spleen sizes. The Bland-Altman plot for comparing the two methods showed mean difference in measures (73 cc) and difference variation (1 S.D. =300cc).Conclusions: Prolate method is a simple and useful alternate method for assessing spleen volume that does not require any specialized software for delineating spleen boundaries. However, the implementation of prolate method is operator dependent and requires precise positioning of digital calipers on images. Future work involves comparing the two methods with respect to change in spleen volume compared to baseline, an assessment performed routinely in pharmaceutical clinical trials. DisclosuresNo relevant conflicts of interest to declare.

Drag coefficient and averaged Nusselt number of a scalene prolate ellipsoid

• Momentum and heat transfer characteristics of a scalene prolate ellipsoid were studied. • Effects of particle shape, orientation and Reynolds number were discussed. • Existing correlations for the drag coefficient and averaged Nu were improved. A cold fluid flowing past a hot stationary scalene prolate ellipsoid is numerically studied via a three-dimensional immersed boundary-lattice Boltzmann model (IB-LBM). First, axisymmetric ellipsoids are considered for verification purposes, and good agreement is found between obtained drag coefficient ( C d ) and averaged Nusselt number ( Nu ) and previously reported results. Subsequently, 81 case studies are conducted by changing shape (2 ≤ Ar 1, Ar 2 ≤ 6) and incident angle (0° ≤ θ ≤ 90°) of the ellipsoid as well as the Reynolds number (25 ≤ Re ≤ 200). In this study, we particularly consider scalene prolate ellipsoids with unequal Ar 1 and Ar 2, which have not been studied in detail before. Effects of different factors on momentum and heat transfer characteristics between solid and fluid phases are understood based on the analysis of numerical results. Available formulas reported in the literature are also briefly reviewed. Finally, new correlations for both C d and Nu are developed using the most important factors with average deviations of 3.875% for C d and 1.598% for Nu , respectively. These proposed correlations can be used to facilitate the phase coupling in the multi-phase flow modelling.

Splenic Volume: Correlation between Ultrasonogram and Standard CT Measurements

Evaluation of splenic enlargement is important in the diagnosis and management of various diseases including liver disease, lymphoma and other primary or metastatic neoplasm. This cross sectional study was conducted in the department of radiology and imaging in Bangladesh Institute of Research and Rehabilitation in Diabetes, Endocrine and Metabolic Disorders (BIRDEM) from July 2007 to June 2009. The main objective of the study was to find out a more accurate sonographic measurement of splenic volume that well correlate with gold standard computed tomography (CT) volume. A total of 228 subjects were included in the study. All the subjects underwent ultrasound and CT examinations for measurement of splenic volume. The mean splenic volume measured by AVL (average length) was 182.62±80.28 cm3 (mean±SD) with range of 45.61-590.93 cm3 and by CT scan was 190.18±77.77 cm3 (mean±SD) with range of 46.52-565.81cm3. Most of the subjects 138(60.5%) had splenic volume 101-200 cm3. Splenic volume was evaluate by CT findings of 228 cases and expressed in cm3. Sonographic splenic volumes were calculated by using the prolate Ellipsoid method AVL (average length) and also expressed in cm3.The mean difference of splenic volume evaluated by CT and sonography was 7.43±5.39 cm3 with standard deviation of 5.39 cm3 measured from average length (AVL). The mean difference of splenic volume evaluated by two modalities measured by average length was statistically significant (pp&lt;0.001).

A 3D DLM/FD method for simulating the motion of spheres and ellipsoids under creeping flow conditions

We present in this article a novel distributed Lagrange multiplier/fictitious domain (DLM/FD) method for simulating fluid-particle interaction in three-dimensional (3D) Stokes flow. The methodology is validated by comparing the numerical results for a neutrally buoyant particle, of either spherical or prolate shape, with the associated Jeffrey's solutions for a simple shear flow. The results concerning two balls, interacting under creeping flow conditions in a bounded shear flow, are consistent with those available in the literature. We will discuss also the interactions of two balls in a bounded shear flow, when these balls are very close initially. For a prolate ellipsoid rotating in a shear flow under the sole effect of the particle inertia, shear plane tumbling is stable, while log-rolling is unstable. For two prolate ellipsoids interacting in a bounded shear flow, the results are similar to those for two balls if the major axes are initially orthogonal to the shear plane (a result not at all surprising considering that the intersections of the ellipsoids with the shear pane are circular).

Shape Effect Analysis of Aluminum Projectile Impact on Whipple Shields

This report presents a numerical analysis study on the shape effects of prolate and oblate ellipsoid projectiles on the performance of spacecraft shields conducted in support of the Orbital Debris Program Office at the NASA Johnson Space Center with the Hypervelocity Impact Technology (HVIT) group [1]. The study served as an independent analysis of the experimental results obtained by the Ernst-Mach Institute, who conducted hypervelocity impact (HVI) tests using shaped-projectiles against a dual-wall Whipple shield to develop ballistic limit equations (BLE) with shape effects. The HVI have been simulated via the three-dimensional, nonlinear-structural-dynamics, simulation tool, CTH, which has been developed by Sandia National Laboratories to treat shock-wave propagation and large-deformation phenomena. The results from the numerical simulations for the sphere and prolate ellipsoid projectiles indicate numerical simulations are a viable tool for conducting HVI analyses, however, significant differences between the CTH models and published EMI test data for the oblate projectiles point to issues in modeling the impact physics of oblate ellipsoid geometries [2]. Consequently, further analysis should be performed to solve the problem in modeling these oblate projectile impacts. The unmodified BLE for spheres and modified BLE for prolate ellipsoids reasonably predict failure of a Whipple shield at low impact velocities, but based on the obtained data may need to be adjusted for velocities between 4 and 8 km/s.

Evaluation of kidney status by ultrasonography in canines: an experimental study

Kidney is a major organ for homeostasis of the body's extracellular fluids by maintaining a constant internal environment. By playing such crucial responsibility kidney remains vulnerable for various diseases and disease condition. Other than laboratory findings, application of ultrasonography can be considered as one of the finest diagnostic tool to determine the architectural detail of kidney. To compare the study, we have taken two groups of canine, namely healthy and clinical. The later grouped was screened based on clinical signs, Blood Urea Nitrogen (BUN) and Serum Creatinine value. Sonography was performed by using Brightness mode instrument for both the groups. The values were analyzed by Prolate Ellipsoid formula to estimate the volume of kidney. There was significant variation in sizes between the kidneys of both the groups. Moreover, the size of the kidneys of few clinical cases, which has been suffering from renal disorder since long, reveals smaller size kidney than the healthy groups. Thus, this noninvasive method is quite practicable to evaluate the size of kidney amongst various renal failure cases. DOI: http://dx.doi.org/10.3329/ralf.v1i1.22373 Res. Agric., Livest. Fish.1(1): 105-108, Dec 2014

An Intensive Review on the Noninvasive Methods to Measure the Urinary Bladder Volume Using Ultrasound Images

Ultrasound is an important diagnostic tool in distinguishing interfaces between soft tissues, especially abdominal structures. Diagnostic ultrasound is used for the detection of cysts, tumors or cancers present in the abdomen. Bladder cancer is one of the common types of cancer nowadays. The volume of the bladder is less in case of presence of cyst, tumors or cancers. Considering the importance of measurement of volume of the urinary bladder, various invasive and noninvasive methods are discussed in this article. The invasive method has many disadvantages. Hence this article encompasses the various noninvasive methods and its implementation using imaging techniques are discussed. The imaging techniques include Prolate Ellipsoid Method, Double Area Method and Double Ellipsoid Method. The methodology which is being generally used to calculate the volume of the urinary bladder is Prolate Ellipsoid Method. The accuracy of the above mentioned methods is reported with relatively larger errors of about 60%. The accuracy can be increased by incorporating sophisticated, expensive 3D software packages and imaging tools.

Measuring stone volume – three‐dimensional software reconstruction or an ellipsoid algebra formula?

To determine the optimal method for assessing stone volume, and thus stone burden, by comparing the accuracy of scalene, oblate, and prolate ellipsoid volume equations with three-dimensional (3D)-reconstructed stone volume. Kidney stone volume may be helpful in predicting treatment outcome for renal stones. While the precise measurement of stone volume by 3D reconstruction can be accomplished using modern computer tomography (CT) scanning software, this technique is not available in all hospitals or with routine acute colic scanning protocols. Therefore, maximum diameters as measured by either X-ray or CT are used in the calculation of stone volume based on a scalene ellipsoid formula, as recommended by the European Association of Urology. In all, 100 stones with both X-ray and CT (1-2-mm slices) were reviewed. Complete and partial staghorn stones were excluded. Stone volume was calculated using software designed to measure tissue density of a certain range within a specified region of interest. Correlation coefficients among all measured outcomes were compared. Stone volumes were analysed to determine the average 'shape' of the stones. The maximum stone diameter on X-ray was 3-25 mm and on CT was 3-36 mm, with a reasonable correlation (r = 0.77). Smaller stones (<9 mm) trended towards prolate ellipsoids ('rugby-ball' shaped), stones of 9-15 mm towards oblate ellipsoids (disc shaped), and stones >15 mm towards scalene ellipsoids. There was no difference in stone shape by location within the kidney. As the average shape of renal stones changes with diameter, no single equation for estimating stone volume can be recommended. As the maximum diameter increases, calculated stone volume becomes less accurate, suggesting that larger stones have more asymmetric shapes. We recommend that research looking at stone clearance rates should use 3D-reconstructed stone volumes when available, followed by prolate, oblate, or scalene ellipsoid formulas depending on the maximum stone diameter.

End-systolic and end-diastolic left atrial volume assessment by two-dimensional echocardiography: a comparison study with magnetic resonance imaging.

The left atrial volume (LAV) is an important indicator of the severity of certain diseases, and measuring LAV through the cardiac cycle may enable the evaluation of various left atrium (LA) functional parameters. The results of two-dimensional (2D) echocardiographic LAV measurement methods vary, and no technique is accepted as being optimal. This study compared the accuracy of end-systolic and end-diastolic LAV measurements by 2D echocardiography with those obtained by magnetic resonance imaging (MRI). Fifty consecutive patients who underwent both echocardiography and MRI due to clinical reasons with nonselective cardiac disease were studied. LAVs by 2D echocardiography were obtained with the prolate ellipsoid (PE), biplane area-length (AL), and modified Simpson's (MS) methods. End-systolic and end-diastolic LAVs calculated by each method correlated significantly with MRI results (P<0.0001). The prolate ellipsoid method provided LAVs that most correlated with MRI results, and the biplane area-length and modified Simpson's methods provided LAVs with small mean differences (<5ml) compared to MRI results. All three methods of 2D echocardiographic LAV measurement provide valuable LAV data, suggesting the possibility of evaluating various LA functional parameters.

Dynamical passage to approximate equilibrium shapes for spinning, gravitating rubble asteroids

Many asteroids are thought to be particle aggregates held together principally by self-gravity. Here we study — for static and dynamical situations — the equilibrium shapes of spinning asteroids that are permitted for rubble piles. As in the case of spinning fluid masses, not all shapes are compatible with a granular rheology. We take the asteroid to always be an ellipsoid with an interior modeled as a rigid-plastic, cohesion-less material with a Drucker–Prager yield criterion. Using an approximate volume-averaged procedure, based on the classical method of moments, we investigate the dynamical process by which such objects may achieve equilibrium. We first collapse our dynamical approach to its statical limit to derive regions in spin–shape parameter space that allow equilibrium solutions to exist. At present, only a graphical illustration of these solutions for a prolate ellipsoid following the Drucker–Prager failure law is available [Sharma, I., Jenkins, J.T., Burns, J.A., 2005a. Bull. Am. Astron. Soc. 37, 643; Sharma, I., Jenkins, J.T., Burns, J.A., 2005b. Equilibrium shapes of ellipsoidal soil asteroids. In: García-Rojo, R., Hermann, H.J., McNamara, S. (Eds.), Proceedings of the 5th International Conference on Micromechanics of Granular Media, vol. 1. A.A. Balkema, UK; Holsapple, K.A., 2007. Icarus 187, 500–509]. Here, we obtain the equilibrium landscapes for general triaxial ellipsoids, as well as provide the requisite governing formulae. In addition, we demonstrate that it may be possible to better interpret the results of Richardson et al. [Richardson, D.C., Elankumaran, P., Sanderson, R.E., 2005. Icarus 173, 349–361] within the context of a Drucker–Prager material. The graphical result for prolate ellipsoids in the static limit is the same as those of Holsapple [Holsapple, K.A., 2007. Icarus 187, 500–509] because, when worked out, his final equations will match ours. This is because, though the formalisms to reach these expressions differ, in statics, at the lowest level of approximation, volume-averaging and the approach of Holsapple [Holsapple, K.A., 2007. Icarus 187, 500–509] coincide. We note that the approach applied here was obtained independently [Sharma, I., Jenkins, J.T., Burns, J.A., 2003. Bull. Am. Astron. Soc. 35, 1034; Sharma, I., 2004. Rotational Dynamics of Deformable Ellipsoids with Applications to Asteroids. Ph.D. thesis, Cornell University] and it provides a general, though approximate, framework that is amenable to systematic improvements and is flexible enough to incorporate the dynamical effects of a changing shape, different rheologies and complex rotational histories. To demonstrate our technique, we investigate the non-equilibrium dynamics of rigid-plastic, spinning, prolate asteroids to examine the simultaneous histories of shape and spin rate for rubble piles. We have succeeded in recovering most results of Richardson et al. [Richardson, D.C., Elankumaran, P., Sanderson, R.E., 2005. Icarus 173, 349–361], who obtained equilibrium shapes by studying numerically the passage into equilibrium of aggregates containing discrete, interacting, frictionless, spherical particles. Our mainly analytical approach aids in understanding and quantifying previous numerical simulations.

Vortical flow between rotating ellipsoids

Experimental results on incompressible viscous flows in the gap between rotating spheroids are presented. Oblate ellipsoids are discussed as a connecting link between a sphere and a disk, while a prolate ellipsoid represents the geometrical intermediate stage between a sphere and a cylinder. The axes ratios of the ellipsoids are A : B=2 : 1 and A : B=1 : 2, respectively. The basic flow field and the occurring instabilities in form of Taylor- and cross-flow vortices have been studied by flow visualization. The common properties and their differences regarding the various flow patterns of the disks, spheres, cylinders as well as of the oblate and prolate ellipsoids are treated. The location of the generation of the different vortex systems at the various rotating bodies is determined. A comparison of the friction torque for these bodies of rotation is given by diagrams. Finally, the theoretically derived curves for the friction torque of the disks, spheres and cylinders are compared with the experimentally obtained data for the oblate and prolate ellipsoids.

Trifluoperazine effects on anionic and zwitterionic micelles: a study by small angle X-ray scattering

In this work small angle X-ray scattering (SAXS) studies on the interaction of the phenothiazine trifluoperazine (TFP, 2–10 mM), a cationic drug, with micelles of the zwitterionic surfactant 3-( N-hexadecyl- N, N-dimethylammonium) propane sulfonate (HPS, 30 mM) and the anionic surfactant sodium dodecyl sulfate (SDS, 40 mM) at pH 4.0, 7.0, and 9.0 are reported. The data were analyzed through the modeling of the micellar form factor and interference function, as well as by means of the distance distribution function p( r). For anionic micelles (SDS), the results evidence a micellar shape transformation from prolate ellipsoid to cylinder accompanied by micellar growth and surface charge screening as the molar ratio TFP:SDS increases in the complex for all values of pH. Small ellipsoids with axial ratio ν=1.5±0.1 (long dimension of 60 Å) grow and reassemble into cylinder-like aggregates upon 5 mM drug incorporation (1 TFP:8 SDS monomers) with a decrease of the micelle surface charge. At 10 mM TFP:40 mM SDS cylindrical micelles are totally screened with an axial ratio ν≈4 (long dimension ≈140 Å at pH 7.0 and 9.0). However, at pH 4.0, where the drug is partially diprotonated, 10 mM TFP incorporation gives rise to a huge increase in micellar size, resulting in micelles at least 400 Å long, without altering the intramicellar core. For zwitterionic micelles (HPS), the results have shown that the aggregates also resemble small prolate ellipsoids with averaged axial ratio ≈ ν=1.6±0.1. Under TFP addition, both the paraffinic radius and the micellar size show a slight decrease, giving evidence that the micellar hydrophobic core may be affected by phenothiazine incorporation rather than that observed for the SDS/TFP comicelle. Therefore, our results demonstrate that the axial ratio and shape evolution of the surfactant:TFP complex are both dependent on surfactant surface-charge and drug:surfactant molar ratio. The results are compared with those recently obtained for another phenothiazine drug, chlorpromazine (CPZ), in SDS and HPS micelles (Caetano, Gelamo, Tabak, and Itri, J. Colloid Interface Science 248 (2002) 149).

The primary electroviscous effect, free solution electrophoretic mobility, and diffusion of dilute prolate ellipsoid particles (minor axis = 3 nm) in monovalent salt solution

The principal objective of the present work is the modeling of the primary electroviscous effect of charged prolate ellipsoid models of low axial ratio. Other transport properties examined include (free solution) electrophoretic mobilities and translational diffusion constants. A numerical boundary element method is employed to solve the coupled Poisson, low Reynolds number Navier–Stokes, and ion transport equations. The methodology is first applied to the primary electroviscous effect of spheres with a centrosymmetric charge distribution and excellent agreement with independent theory is obtained. Specific model studies are also carried out for prolate ellipsoid models with axial ratios less than 4 and a minor axis equal to 3 nm. Most studies are carried out in aqueous NaCl solution (2 to 50 mM) at 20 °C for a range of different particle charges, although limited results are also presented in LiCl and KCl solution. The primary electroviscous effect for weakly charged prolate ellipsoids is smaller than that of a sphere under similar conditions. These studies are also carried out at high absolute particle charge. A comparison is made between the primary electroviscous effect and electrophoretic mobilities of prolate ellipsoids and corresponding spherical models.

Chlorpromazine and Sodium Dodecyl Sulfate Mixed Micelles Investigated by Small Angle X-Ray Scattering

Small-angle X-ray scattering (SAXS) studies are reported on the interaction of chlorpromazine (CPZ) with micelles of anionic surfactant sodium dodecyl sulfate (SDS). Isotropic solutions of SDS (40 and 100 mM) at pH 4.0, 7.0, and 9.0 in the absence and presence of CPZ (2–25 mM) were investigated at the National Laboratory of Synchrotron Light (LNLS, Campinas, Brazil). The data were analyzed through the modeling of the micellar form factor and interference function. The results evidence a micellar shape transformation from prolate ellipsoid to cylinder accompanied by micellar growth and surface charge screening as the molar ratio CPZ : SDS increases in the complex. Small ellipsoids with axial ratio ν=1.5±0.1 at 40 mM SDS grow and reassemble into cylinder-like aggregates upon 5 mM drug incorporation (1 CPZ : 8 SDS monomers) with a decrease of the micelle surface charge. At 10 mM CPZ : 40 mM SDS cylindrical micelles are totally screened with an axial ratio ν≈2.5. The data also indicate the presence of small prolate ellipsoids (ν=1.7±0.1) in solutions of 100 mM SDS (no drug) and micellar growth (ν≈2.0 and 4.0) when 10 and 25 mM CPZ are added to the system. In the latter case, the aggregate is also better represented by a cylinder-like form. Therefore, our results demonstrate that the axial ratio and shape evolution of the surfactant : phenothiazine complex are both SDS concentration and drug : SDS molar ratio dependent. The drug location close to the SDS polar headgroup region without disrupting in a significant way both the paraffinic hydrophobic core and the polar shell thickness is inferred. SAXS data made it possible to obtain the shapes and dimensions of CPZ/SDS aggregates.

Molecular simulation of liquid-crystal transitions in hard prolate ellipsoid monomers and dimers

Molecular simulation results are reported for the liquid-crystal phase transitions of both monomers and dimers of hard prolate ellipsoids. The effect of different elongations ( γ) is studied. In contrast to earlier work, evidence is found for the onset of isotropic-ordered phase transitions for monomers of relatively small elongations, although the transition is not stable. Dimers of prolate hard ellipsoids behave very differently to ellipsoid monomer of equal size. In the dimer case, a clear isotropic-ordered phase transition is observed whereas such a clear transition is absent in monomers.