Frontal Angle: A New Predictor of Difficulty in Endoscopic Frontal Sinus Surgery—A Preliminary Computed Tomography Study

Objectives: The possibility of visualization of the frontal sinus during endoscopic surgery depends on 3-dimensional configuration of the frontal sinus opening (FSO). We aimed to determine the prevalence of unfavorable angulation of the lower part of the posterior wall of the frontal sinus and its relation to FSO diameter. Methods: One hundred and twenty-eight computed tomography (CT) scans were retrospectively reviewed to measure (1) the angle between the nasal floor and the plane tangent to the posterior table of the frontal sinus above the most posterior aspect of the anterior buttress (frontal angle, FA) and (2) dimensions of the FSO. Results: The FA ranged from below 30° to 90°. Nearly 13% of sinuses (16.4% of patients) showed FA about 90°, which should enable good visualization of the sinus with the 30° scope after opening and clearing the frontal recess, while 4% (6.25% of patients) showed FA ≤ 30°. The anterior–posterior diameter (A-PD) was below 5 mm in 17.6% of sinuses (26.6% of patients). There was a significant correlation between FA and A-PD. Unfavorable combination of FA and A-PD (<45°, <5 mm) was present in 5.2% of sinuses (8.6% of patients), and extremely unfavorable combination (<30°, <5 mm) in 0.8% (0.8% of patients). Conclusions: The FA shows great interindividual variability, which is very likely to reflect the possibility of inspection of the frontal sinus. This implies a need for further prospective clinical studies to validate FA as a predictor of difficulty in frontal sinus surgery.

Plane Tangent to Quasi-Rotation Surface

The analysis of a surface generated by quasi-rotation of a straight line around a circle is provided in the present paper. The considered case features a straight generatrix belonging to the plane of a circular axis of quasi-rotation and intersecting it in two points. A geometric method of determination of a point belonging to a surface given its projection on the axis plane is demonstrated. Geometric construction of the curves of intersection between the considered surface and a conic surface is presented. A method of determination of points belonging to the considered surface as points belonging to the curve of intersection of two conic surfaces is acquired. Step-by-step constructions illustrating the solution of the problem of determination of a plane tangent to the considered surface in a given point are provided. The problem is solved through the methods of descriptive geometry. Every construction is performed according to an analytic algorithm, not involving approximate methods of determination of the sought points. The construction is carried out in a CAD system through the use of tools “straight line by two points” and “circle by center and point”. The presented solution to the defined problem is connected to the solution to the problem of determination of the rays reflected from the considered surface. The results of the paper expose the geometric properties of surfaces of quasi-rotation. The provided constructions can serve as the basis for the research of optical properties of the considered surfaces.

Post-traumatic temporal lobe lesions: surgical decision making based on CT scan findings

BACKGROUND: The indication for surgical treatment of post-traumatic parenchymal lesions in the temporal lobe remains controversial. OBJECTIVE: We reviewd the tomographic parameters that might be useful in making surgical decisions. METHOD: The tomographic findings of 69 patients were analyzed in a retrospective manner considering: 1) the effects of the lesion (classified into 4 variables: midline shift, status of the cisterns, status of the ventricles, and status of the peripheral sulci); and 2) the characteristics of the lesion: anterior, posterior or anteroposterior location (as defined by a coronal plane tangent to the cerebral peduncles) and its mediolateral diameter. RESULTS: When none or only one of the aforementioned variables was found to be altered, conservative treatment was instituted (22 out of 38 lesions). In two cases, all four variables were altered, and surgery was performed in both. Anterior, anteroposterior and posterior lesions measuring 21, 23 and 28 mm in diameter, respectively, had a 50% chance of surgical removal. CONCLUSION: Amongst the patients who underwent surgical intervention, the more anterior the location of the temporal lobe lesion, the smaller the diameter.

Astrogeodetic Fix by Azimuth Differences; Solution in Rectangular Coordinates

This paper offers a precise and almost final solution to one of the most debated problems connected with the astrogeodetic ‘fix’ by azimuth differences. The rectangular and linear solution on the gnomonic plane, tangent to the celestial globe and the dead reckoning position, enables the use of azimuth differences and is connected to Pothenot's solution. Thus this problem may be solved with simple linear algorithms that require neither differential modes, nor the introduction of the unknown origin error.

A Computer Aided Geometric Method for Development of Conical Convolutes

Convolutes are single curved, ruled surfaces formed by moving a plane tangent to two curves called the directrices. Conical convolutes are one form of convolutes. If atleast one of the two planar directrices is a super-ellipse, then the surface is called a super-conical convolute. Necessary mathematical expressions for the geometrical details as well as the development of the super-conical convolute surface are given in this paper. Also a suitable algorithm for the development of the surface is given. An illustrative case study is presented.

Slow oscillations in an ocean of varying depth Part 2. Islands and seamounts

We consider slow oscillations trapped about axisymmetric islands and seamounts. ω is in the range [lsim ] δ/2 (ω is the frequency divided by f, the Coriolis parameter, and δ the fractional change in depth). The periods, for example, are [gsim ] 2·4 days for an island with a sloping ‘skirt’, h [vprop ] r½, where h is the depth and (r, θ) are polar co-ordinates in the plane tangent to the mean sea surface. Energy leaks slowly away from the topography in Rossby waves. In the limiting case of a cylindrical island with vertical walls there are no such trapped motions, but incident Rossby waves are scattered anisotropically. If γ, the ratio of the island radius, a, to the Rossby wavelength, is small, the scattering cross-section ∼ γ3a. The free oscillations at seamounts and islands with skirts allow much stronger scattering (with cross-section ∼ a/γ, ∼ a wavelength), when one of their frequencies is near that of the incident wave.The theory suggests that measurements of Rossby waves will be possible at small islands, but that the many local oscillations in the same frequency range will add some confusion.