This study verifies the three-dimensional anatomical features of the transverse and alar ligaments with reference to the axis using a direct in vitro approach. In 20 fresh spine specimens, metal markers were inserted on the cranium, atlas, and axis. After registration of the intact specimen, the bony segments were separated, and markers and anatomical landmarks were digitized. The length and the orientation of the ligaments with reference to the axis were derived from the relative position data. The transverse ligaments of the atlas have a mean estimated length of 21 mm and an absolute angle (i.e., independent of any reference frame) of 119 degrees +/- 17 degrees . The alar ligaments have a mean length of 9 +/- 2.5 mm, and the mean absolute angle between the ligaments is 117 degrees +/- 31 degrees . The plane of the alar ligaments shows a mean backward inclination of -10 degrees +/- 52 degrees . This plane has a mean inclination of 6 degrees +/- 4 degrees with reference to the sagittal plane indicating left-right symmetries. The transverse ligament arches around the dens and demonstrating its function as a stabilizer for the dens as well as guidance for axial rotation movements. A posterior inclination of the alar ligaments may induce a coupled extension in combination with a lateral bending during axial rotation. These detailed aspects of motion steering may be important to consider when attempting to reduce or restore movement.

There seems to be a strong relationship between the anatomic features of the lateral articulating surfaces of atlas and axis. Differences in the orientation of joint surfaces to the frontal plane may be related to deviations from the neutral position. This issue raises the problem of the definition of three-dimensional-neutral joint positions.

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An axial compressor end-wall boundary layer theory which requires the introduction of three-dimensional velocity profile models is described. The method is based on pitch-averaged boundary layer equations and contains blade force-defect terms for which a new expression in function of transverse momentum thickness is introduced. In presence of tip clearance a component of the defect force proportional to the clearance over blade height ratio is also introduced. In this way two constants enter the model. It is also shown that all three-dimensional velocity profile models present inherent limitations with regard to the range of boundary layer momentum thicknesses they are able to represent. Therefore a new heuristic velocity profile model is introduced, giving higher flexibility. The end-wall boundary layer calculation allows a correction of the efficiency due to end-wall losses as well as calculation of blockage. The two constants entering the model are calibrated and compared with experimental data allowing a good prediction of overall efficiency including clearance effects and aspect ratio. Besides, the method allows a prediction of radial distribution of velocities and flow angles including the end-wall region and examples are shown compared to experimental data.