Radial Plane Research Articles

Stomatal development and patterning in Arabidopsis leaves

The functional unit for gas exchange between plants and the atmosphere is the stomatal complex, an epidermal structure composed of two guard cells, which delimit a stomatal pore, and their subsidiary cells. In the present work, we define the basic structural unit formed in Arabidopsis thaliana during leaf development, the anisocytic stomatal complex. We perform a cell lineage analysis by transposon excision founding that at least a small percentage of stomatal complexes are unequivocally non‐clonal. We also describe the three‐dimensional pattern of stomata in the Arabidopsis leaf. In the epidermal plane, subsidiary cells of most stomatal complexes contact the subsidiary cells of immediately adjacent complexes. This minimal distance between stomatal complexes allows each stoma to be circled by a full complement of subsidiary cells, with which guard cells can exchange water and ions in order to open or to close the pore. In the radial plane, stomata (and their precursors, the meristemoids) are located at the junctions of several mesophyll cells. This meristemoid patterning may be a consequence of signals that operate along the radial axis of the leaf, which establish meristemoid differentiation precisely at these places. Since stomatal development is basipetal, these radially propagated signals may be transmitted in the axial direction, thus guiding stomatal development through the basal end of the leaf.

Radial focusing of ion beams in a mass analyzer with an electrostatic lens and a sector-shaped inclined-wall magnetic prism

The ionic and optical properties of an inclined-wall magnetic mass analyzer with electrostatic direction focusing of ions in a nonuniform (r−1) magnetic field were studied. A condition for ion focusing in the radial plane was derived, and the basic parameters of the mass analyzer were determined.

Macroscopic diffusional anisotropy in porous media

An image analysis method, based on a lattice-based model projection technique, has been used to show that the structure of a porous catalyst support pellet may possess a fractal character over macroscopic lengthscales (0.01–1 mm). It has also been shown that a geometric method of obtaining tortuosity for lattice-based model structural representations (such as those used in the image analysis method) gives rise to a good prediction of the degree of anisotropy to be expected between the diffusion in the axial and radial planes of the cylindrical pellet.

Endocarp Dehiscence in Pistachio (Pistacia vera L.).

Two sites exist for endocarp dehiscence (shell split) in the pistachio nut (Pistacia vera L., Anacardiaceae). Longitudinal dehiscence occurs along lines of cells that have highly lignified, interlocking walls and are differentiated from cells of the neighboring endocarp only by being somewhat smaller and slightly elongate in the radial plane. Apical dehiscence occurs at the site where transmitting tissue penetrates the ovary wall to enter the ovarian locule. In most fruits, cells delineating the line of apical dehiscence possess thin, primary walls that stain only diffusely for pectic materials. In rare cases, possibly when apical dehiscence fails, these cells become lignified. Measurements of seeds and inner dimensions of endocarps of mature fruits show that dehiscent endocarps differ from indehiscent endocarps by having more massive seeds and seeds that are larger relative to the size of the endocarp. These results and observations indicate to us that two dehiscence events occur: longitudinal shell split, which is driven by physical forces exerted on the endocarp by the seed, and apical dehiscence, which occurs at the site of intrusion of the transmitting tissue tract into the ovary and varies according to the extent of transmitting tissue present at anthesis as well as the degree of cytodifferentiation that may occur in these cells.

Radial-sequence magnetic resonance imaging in evaluation of acetabular labrum

We investigated the usefulness of a radial-sequence magnetic resonance imaging (MRI) technique in the visualization of the acetabular labrum, which surrounds the acetabulum. In 22 hip joints of 12 volunteers, T2-weighted images were obtained on 24 radial planes of the acetabular rim, set at 15°-intervals, using the small tip angle gradient echo method. We examined 7 planes in the weight-bearing portion. The acetabular labrum in the weight-bearing portion was depicted in good contrast to the surrounding tissues. The shape of the labrum differed among individuals and also in the anterior and posterior portions of the labrum. The signal intensity of the labrum was low or partially moderate. There was a high signal intensity band on the base of the acetabular labrum in several portions, which should be carefully interpreted to avoid confusion with abnormality. We concluded that radial-sequence MRI could be a useful technique for evaluation of the condition of the acetabular labrum in the weight-bearing portion.

MR arthrography of the labrum acetabulare--a radiological-anatomical correlation in 20 cadaveric hips

To investigate frequency of acetabular labral lesions in elderly hip joints, and to determine sensitivity and specificity of MR arthrography (MRa) for the detection of these abnormalities. Twenty cadaveric hip joints were examined by MRa. For MRa, 15 ml of a solution of iodinated contrast solution (Solutrast 300) and Gd-DTPA (100:1) were injected under fluoroscopic guidance. MR imaging was performed on a 1.5 T MR scanner (Vision, Siemens; FOV 16 cm, matrix 256 x 256, fat-suppressed 3D-FLASH). Multiplanar image reconstructions were done perpendicular to the acetabulum in the oblique-coronal, oblique-axial, and radial planes. The labral specimens were examined macroscopically. In 12/20 hips (60%), a labral lesion was found on pathologic examination. In 7 specimens, the labrum was partially or completely detached in the weight-bearing superior region. One flap-like variant of the labrum was seen; in 4 hip joints, the labrum was degenerated (one cystic degeneration). Pathologic findings were confirmed by MRa in 8/12 specimens (sensitivity 67%). All degenerated labra were correctly diagnosed on MRa. Three small labral detachments and the flap-like variant were misinterpreted as being normal. There were no false positive findings (specificity 100%). The accuracy was 80%. Labral lesions were seen in 6/8 and in 6/12 of hips with and without osteoarthritis, respectively. MRa is well suited to delineate the acetabular labrum and to diagnose labral abnormalities. Detection of small labral detachments and anatomic variants is difficult and requires some experience. Labral lesions are correlated to osteoarthritis of the hip, but may be frequently seen in the elderly without underlying osteoarthritis.

A radiotracer application for the turbulent dispersion of fluids

The concentration profiles for turbulent flow were determined using a radiotracer technique. An experimental test device was constructed and sodium-24 was used as the tracer. Methylene-blue was also used for a comparison of the results. Samples were taken from different radial planes. The mean squared displacement was calculated and compared with the data of Taylor and Middleman [Taylor, A.R., Middleman, S., 1974. Turbulent dispersion in drag-reducing fluids. AIChE Journal, 20(3), 454-461]. It was shown that the radiotracer technique could be applied successfully to turbulent flow in vertical pipes.

Structure and dynamics of the wake of bubbles and its relevance for bubble interaction

The flow in the wake of single and two interacting air bubbles freely rising in water is studied experimentally using digital-particle-image-velocimetry in combination with high-speed recording. The experiments focus on ellipsoidal bubbles of diameter of about 0.4–0.8 cm which show spiraling, zigzagging, and rocking motion during their rise in water, which was seeded with small tracer particles for flow visualization. Under counterflow conditions in the vertical channel, the bubbles are retained in the center of the observation region, which allows the wake oscillations and bubble interaction to be observed over several successive periods. By simultaneous diffuse illumination in addition to the light sheet, we were able to record both the path and shape oscillations of the bubble, as well as the wake structure in a horizontal and vertical cross section. The results show that the zigzagging motion is coupled to a regular generation and discharge of alternate oppositely oriented hairpin-like vortex structures. Associated with the wake oscillation, the bubble experiences a strong asymmetric deformation in the equatorial plane at the inversion points of the zigzag path. The zigzag motion is superimposed on a small lateral drift of the bubble, which implies the existence of a net lift force. This is explained by the observed different strength of the hairpin vortices in the zig and zag path; a seemingly familiar phenomenon was found in recent numerical results of the sphere wake flow. For spiraling bubbles the wake is approximately steady to an observer moving with the bubble. It consists of a twisted pair of streamwise vortex filaments which are wound in a helical path and are attached to the bubble base at an asymmetrical position. The minor axis of the bubble is tilted in the tangential plane as well as in the radial plane toward the spiral center. Due to the pressure field induced by the asymmetrically attached wake two components of the lift force exist, one that causes the lateral motion and the other a centripetal force that keeps the bubble on a circular path. A mechanism is proposed to explain the reason for one bubble to spiral or to zigzag. Experiments with two simultaneous released bubbles show that bubble interaction is strongly triggered by the wake dynamics. Once a bubble is captured in the wake of a rocking bubble, it accelerates and rises via successive jumps until they collide. The jumps are explained by the upwards induction effect of the ring-like heads of the hairpin vortices being shed from the leading bubble. The final collision and repulsion thereafter abruptly enlarges the wake for a short moment, which is suggested to be one major contribution to the amplification of turbulence production in bubbly flows.

Spacetime Embedding Diagrams for Black Holes

We show that the 1 + 1 dimensional reduction(i.e., the radial plane) of the Kruskal black hole canbe embedded in 2 + 1 Minkowski spacetime and discuss howfeatures of this spacetime can be seen from theembedding diagram. The purpose of this work iseducational: The associated embedding diagrams may beuseful for explaining aspects of black holes to studentswho are familiar with special relativity, but notgeneral relativity.

Suitability of acetylated woods for clarinet reed

The density (ϱ), dynamic Young's modulus (E), loss tangent (tanδL) in the longitudinal (L) direction, and the dynamic shear modulus (G), loss tangent (tanδS) in the LT or LR (T, tangential; R, radial) plane of woods and cane (Arundo donax L.) in air-dried and wet conditions were measured. The acoustic converting efficiency (ACE), expressed by √E/ϱ3/tanδL, and the factors of anisotropy, expressed byE/G and tanδS/tanδL, of woods were compared with those of the canes. Low-density coniferous woods had higher ACE values and were of a more anisotropic nature than the cane. These woods seemed appropriate for clarinet reed owing to their homogeneous cellular structure. The stability in vibrational properties and the anticreep properties of the woods were enhanced by the acetylation treatment. Professional clarinet players suggested that acetylated Glehn's spruce and sitka spruce were suitable for clarinet reeds.

Endoluminal MR imaging of the rectum and anus: technique, applications, and pitfalls.

Anorectal diseases (e.g., fecal incontinence, perianal and anovaginal fistulas, anorectal tumors) require imaging for proper case management. Endoluminal magnetic resonance (MR) imaging has become an important part of diagnostic work-up in such cases. Optimal endoluminal MR imaging requires careful attention to patient preparation, imaging protocols, and potential pitfalls in interpretation. Comfortable positioning and the use of an antiperistaltic drug are vital for adequate patient preparation. Selected sequences and imaging planes are used in imaging protocols tailored for specific diseases. In fecal incontinence, three-dimensional sequences allow detailed demonstration of the anal anatomy and related defects. In perianal and anovaginal fistulas, longitudinal imaging planes help determine the superior extent of the abnormality. In anorectal tumors, T1-weighted turbo spin-echo MR imaging can help detect extension into the perirectal fat and T2-weighted turbo spin-echo MR imaging is used to optimize contrast between tumor and the rectal wall. Off-axis and radial imaging planes are used in all anorectal diseases to minimize partial volume effects. Potential pitfalls include various parts of the normal anal anatomy mimicking sphincter defects, veins and hemorrhoids mimicking fistulas and abscesses, and overhanging tumor mimicking more extensive tumor. Adequate patient preparation combined with proper technique and a knowledge of potential pitfalls will allow optimal endoluminal MR imaging of the rectum and anus.

BUOYANT FLOW GENERATED BY THERMAL CONVECTION OF A SIMULATED PIG

The effects of internal occupants and supplement heating make up an essential issue for the prediction andcontrol of fresh ventilating air distribution in an enclosure. The influence from livestock is complex, since they are mobileobstacles, producing heat and contaminants in irregular geometry. As a part of the basic studies of these influences, theinvestigations of air motion in a thermal buoyant flow caused by free convection around a livestock body are reported inthis article. A simulated pig, made of a painted metal tube (1 m long and 0.5 m in diameter) with covered ends and heatelements inside, was used as the heat source in the experiments. The experiments were carried out in a full-scale room, 5m 11 m in floor area, with a 2.4 m side wall height, and sloped ceiling to center (height: 4.8 m). The simulated pig wasplaced near the center of the floor. The vertical temperature difference in the room space was less than 0.3C. Thevelocity and temperature in the thermal plume were measured with six sensors (each has both temperature and velocityelements) placed at 0.2 m horizontal intervals. Data were acquired at 14 levels from 0.2 to 2.4 m above the top surface ofthe simulated pig. The data-sampling period was 30 min in steady state for each measurement.The results show that the plume was quite thin at the beginning (yd 0.6 m) in the central radial plane of the model.Observations showed that the laminar flow at the beginning remained for some distance before it became turbulent andspread. When the distance from the top of the model increased (yd 0.8 m), the temperature and velocity profile of the jetfit Gaussian distributions. The temperature profiles were slightly wider than the velocity profiles. Numerical simulations(Computational Fluid Dynamics) were applied for the same experimental set-up in computing the airflow over the pigsimulator. Transient simulation with fixed time stepping provided similar results to the measurements, indicating the CFDsimulation method used in the study has potential for prediction of buoyant flow generated by this type heat source.

Endoanal MRI of perianal fistulas: the optimal imaging planes.

Twenty consecutive patients with the clinical suspicion of a perianal fistula were studied to define the optimal and time-efficient imaging planes for endoanal MRI in the identification and classification of perianal fistulas. The duration of each part of the MR procedure was recorded in all patients. Off-axis axial (A), coronal (C), sagittal (S) and radial (R) T2-weighted sequences were performed in all patients. Sets of images and combinations of images (A; R; CS; AR; ACS; ARCS) without patient data were reviewed in masked fashion and independently with a 2-month interval between each set. The reader was masked to the results of previous readings. The findings were compared with the surgical findings. The number of correctly identified and classified fistula and the sensitivity and specificity were determined. Twenty fistulas were present at surgery: 14 transsphincteric fistulas and six intersphincteric fistulas. Eighteen fistulas were correctly identified with the radial (R) and combined coronal sagittal (CS) sequences. In all other sequences or combinations of sequences all 20 fistulas were identified. Classification was correct with A in 16 patients, with R in 15, with CS in 15, with AR in 18, with ACS in 17 and with ARCS in 18. The sensitivity and specificity were optimal using AR or ARCS (0. 86 and 1 respectively). The optimal and most time-efficient imaging protocol for endoanal MRI of perianal fistulas thus comprises the axial and radial imaging planes.

Asymptotics of the eigenvalues of the rotating harmonic oscillator

The eigenenergies λ of a radial Schrödinger equation associated with the problem of a rotating harmonic oscillator are studied, these being values which admit eigensolutions which vanish at both the origin (a regular singularity of the equation) and at infinity. Asymptotic expansions, for the case where a coupling parameter α is small, are derived for λ. The approximation for λ consists of two components, an asymptotic expansion in powers of α, and a single term which is exponentially small (which can be associated with tunneling effects). The method of proof is rigorous, and utilizes three separate asymptotic approximations for the eigenfunction in the complex radial plane, involving elementary functions (WKB or Liouville-Green approximations), a modified Bessel function and a parabolic cylinder function.

Ultrasonic determination of the elastic modulus of human cortical bone.

The elastic modulus (Cii) of the cortical bones of 19 individuals (14 femurs and 16 tibias, fixed in formalin) was determined ultrasonically. Elastic moduli were measured at four anatomical positions (anterior, posterior, medial and lateral) and in all three planes of orientation (transverse, longitudinal and radial). The mean tibial Cii (34.11 GPa) was greater than that obtained for femurs (32.52 GPa). The tibial longitudinal plane Cii (34.1 GPa) was significantly greater than the femoral longitudinal plane Cii (32.5 GPa). Cii was significantly higher in the tibia than the femur in both the medial and posterior anatomical positions. The anterior tibia had a significantly lower C11 compared to other positions. Cii was significantly higher in the longitudinal plane than the transverse or radial planes in both the femur and the tibia. There was no consistent difference in modulus between left and right sides. No age effects were observed. There were no significant differences between males and females, or between African Americans and European Americans.

Entry Flow Patterns for Polymer Solutions through Eccentric Abrupt Contractions.

Flow visualizations using the two kinds of tracer methods and LDV measurements with shearthinning aqueous solutions of polyacrylamide through an axisymmetric contraction and two eccentric contractions have been carried out. In these experiments the effect of contraction eccentricity on flow patterns has been studied. In the steady regime the largest vortex length for the eccentric contractions is almost the same as that for the axisymmetric contraction ; on the other hand, within the vortex the streak line circulates in a radial plane for the axisymmetric contraction while it spirals from the minimum vortex region toward the maximum one for the eccentric contractions. Furthermore, a small-scale instability occurs near the boundary between main flow and upstream end of vortex. Finally the main flow spirals both for the axisymmetric and eccentric contractions in entirely unstable flow regime.

Probing radial and axial secular frequencies in a quadrupole ion trap

We simulate an operating mode in which the ions are introduced inside a quadrupole trap and slowed down to be confined; after a given confinement time, they are ejected out of the trap towards the detector through the upper end-cap. This elementary experiment is repeated for a set of increasing confinement times. The temporal ion signal obtained is an image of the confined ions' motion. This signal, which is periodical, contains the radial and/or axial secular frequencies of all the confined ionic species depending on the mode of detection. In previous papers, we have shown that with a large circular exit hole centred on the z axis of the trap and with a numerical treatment of the ion time-of-flight (TOF) histogram recorded for each confinement time, we obtain only the z secular frequency. In this paper, we show that the exit position of an ion in the radial plane depends principally on its radial position at the end of the confinement. For this, simply by reducing the dimension of the centred exit hole or by decentring it and counting only the number of ions passing through the hole, we can obtain evidence on the radial secular frequencies. Also, this simulation work allows one to clarify the best operating conditions to measure the x-secular frequencies, that is a decentred exit hole tangential to the oz axis and an ion cloud the excursion of which along the ox axis is limited to the radial position of the exterior edge of the hole and with an ox dimension about three times lower than the hole diameter. In this case, the amplitude calibration is possible as the frequency peak amplitude is proportional to the square value of the mean number of created ions. Moreover, we give the signal over noise ratio under usual values of the operating parameters. This operating mode and its two associated modes of detection could be an useful tool to measure ion motion secular frequencies along the oz axis and along any radial directions. Besides mass spectrometry, the determination of the frequencies shifts and couplings related to the ion motion can lead to other important applications.

Transport in a hollow cylindrical membrane

A detailed treatment has been given of radial transport in and through a hollow cylindrical membrane for two initial distributions of diffusant within the membrane of practical interest. Expressions are given for concentration distributions of diffusant and for unit length of membrane, amounts present, fluxes through radial planes, and amounts transported up to time t across those planes. Some consideration has been given to forward and reverse flow and to relations between flow quantities characteristic of those transports. © 1997 John Wiley & Sons, Inc.

Quantitative evaluation of myocardial single-photon emission tomographic imaging: application to the measurement of perfusion defect size and severity.

A new method is described for precise quantitative analysis of the relative three-dimensional distribution of myocardial tracers. The system uses a 360 degrees elliptical sampling of radial slices to create activity profiles. These are then positioned onto a common centre at the same angular coordinates as the corresponding radial slice reconstruction planes to generate a two-dimensional polar summary display. Abnormal distribution is then identified by automatic comparison of the patient polar map with the threshold of a normal database defined on a pixel by pixel basis as the normal mean -2.5 SD. Our stress and rest databases currently comprise 34 and 24 studies for sestamibi and tetrofosmin respectively. The present method differs from currently available software in two major respects. First, radial slices are used rather than short-axis slices to minimize operator intervention and to allow quantitative evaluation of the left ventricle volume independent of the heart size and without truncation, in particular near the apex and at the base. This sampling scheme also results in a more homogeneous and sampling-independent partial volume effect. Secondly, quantitative analysis is improved by calculating perfusion defect severity, extent and size in a precise manner. Severity is evaluated relative to a standardized background measurement and to the mean normal value rather than to the threshold value. This parameter was underestimated up to a defect extent of 32 cm2 in our phantom studies. Calculation of defect extent takes into account the surface distortion resulting from planar projection by using pixel by pixel weighted factors but it is otherwise overestimated as a result of the limited resolution of the imaging system. Integrating defect severity and extent, our hypoperfusion index appeared to accurately estimate the true defect size in our phantom model (r=0.993). The reproducibility of analysis was 6.24% in phantom studies and 3.10% in patient studies including repeated acquisitions. Applied to a well-documented population of 80 patients, this method resulted in an 86% sensitivity and a 78% specificity for overall coronary artery disease detection with reference to the angiographic data.

A well-type ionization chamber geometric correction factor

To correct for the influence of source configuration on the measured activity of spherical and cylindrical brachytherapy sources, a geometric correction factor was calculated for the Standard Imaging HDR-1000 well-type ionization chamber. A Fortran program modelled each source as a lattice of point sources. Because of the cylindrical symmetry of the well chamber, it could be uniquely modelled by point detectors along the perimeter of the radial plane of the detection volume. Path lengths were calculated and attenuation factors were applied to each source - detector point combination individually. The total dose rate at each detection point was found through a Sievert summation of the point source contributions. For sources with identical activities, a correction factor of was calculated, equal to the ratio of the dose rate of the cylindrical source to that of the sphere. Experimental verification using a Nuclear Associates 67-809 series cylindrical source and an Amersham spherical source yielded a correction factor of .