Longitudinal Angle Research Articles

A comparison of two different techniques in the surgical treatment of flexible pes planovalgus: calcaneal lengthening and extra-articular subtalar arthrodesis

The objective of this study was to compare the results of calcaneal lengthening and Dennyson-Fulford extra-articular subtalar arthrodesis operations performed in patients with flexible pes planovalgus owing to various etiologies and to compare their effectiveness in realigning the foot. Two patient groups were retrospectively formed out of the patients in whom calcaneal lengthening (25 feet of 13 patients) and subtalar extra-articular arthrodesis (27 feet of 15 patients) operations were performed. The modified Evans technique for the calcaneal lengthening operation and the Dennyson-Fulford technique for the subtalar extra-articular arthrodesis operation were applied. Any special criterion to choose the indication was not considered. The main indication for the surgery was pain during daily routine activities in both groups. The patients were evaluated preoperatively and during the last visit, both clinically and radiographically. The groups were homogenous for sex and mean age for the process, but in the subtalar extra-articular arthrodesis group, the deformity was more severe in some parameters, mean follow-up period was significantly longer and neurologic etiologies were more dominant. Anteroposterior talocalcaneal and talonavicular angles were worse in the subtalar extra-articular arthrodesis group preoperatively (P<0.05). Both groups showed significant correction (P<0.05) in all parameters postoperatively. In the last visit, lateral talocalcaneal, anteroposterior, and lateral talonavicular angles were worse in the calcaneal lengthening group (P<0.05) and calcaneal pitch angle was worse in the subtalar extra-articular arthrodesis group (P<0.05). Both groups showed significant clinical correction (P<0.05) in all parameters postoperatively, but there was no significant difference between the groups during the last visit in terms of total clinical scores (P>0.05). Pain, the parameter that was the main indication for surgery, was eliminated in all patients except for one in the calcaneal lengthening group. The evaluation of the effectiveness of the surgical technique on the results made by performing repeated measures from general linear models showed significantly better correction in anteroposterior and lateral talocalcaneal angles, anteroposterior and lateral talonavicular angles, and medial longitudinal arc angle in the subtalar extra-articular arthrodesis group (P<0.05). In conclusion, in this study group, the subtalar extra-articular arthrodesis technique was superior in talocalcaneonavicular joint complex reduction and medial longitudinal arc reconstruction in the surgical treatment of flexible pes planovalgus, and calcaneal lengthening provided better correction of calcaneal equinus. Therefore, it is better to use the calcaneal lengthening technique in mild or moderate deformities because of its physiological advantages, and subtalar extra-articular arthrodesis technique in severe and/or rigid deformities because of its superior potential to correct the deformity and stabilize the foot in the corrected position.

Regression modeling method of space weather prediction

A regression modeling method of space weather prediction is proposed. It allows forecasting Dst index up to 6 hours ahead with about 90% correlation. It can also be used for constructing phenomenological models of interaction between the solar wind and the magnetosphere. With its help two new geoeffective parameters were found: latitudinal and longitudinal flow angles of the solar wind. It was shown that Dst index remembers its previous values for 2000 hours.

TU‐C‐BRD‐06: Preclinical Image Guided Microirradiators: Concepts, Design and Implementation

We will introduce small animal image guided microirradiators by reviewing the concepts and requirements for high resolution and high conformality irradiation of tumors implanted in small animal limbs (xenograft tumor models), animal organs and spontaneous tumor models. We will present two preclinical microirradiators developed by our group, a brachytherapy based microirradiator and an orthovoltage x‐ray source based microirradiator. The brachytherapy irradiator has been constructed around a commercial high‐dose rate (HDR) remote afterloader source in a teletherapy geometry. The system consists of a set of exchangeable tungsten collimators (from 2.5 to 5.5 mm diameter) mounted on an aluminum cylindrical support. An HDR catheter is then used to transport the source to the pre‐determined dwell position that centers the source at the collimator hole. With this microirradiator, the anatomical image is obtained using an external clinical CT operated at maximum resolution and coregistration is achieved using fiducial markers.The x‐ray orthovoltage microirradiator has an onboard cone beam microCT subsystem for submillimeter low dose anatomical imaging. The microCT and the ontrovoltage x‐ray source are aligned using a common rotation axis in a tandem configuration. An axial motorized animal bed transfers the animal from the microCT subsystem to the microirradiation subsystem. The microCT subsystem was constructed using an 80 kVp micro‐focus x‐ray source with a 75 × 75 um2 focal spot and a flat panel amorphous silicon detector with 1024 × 1024 pixels. The orthovoltage irradiator subsystem was constructed using a 320 kVp x‐ray source with dual focus spots (0.4 × 0.4 mm2 at 800W and 1 × 1 mm2 at 1800 W). The orthovoltage beam is collimated using orthogonal jaws and exchangeable apertures. The treatment beam can be aimed at different latitudinal and longitudinal angles in steps of 2 arcmin. and translated at 100 μm steps (x, y and z). The beam cross sections can be modulated with submillimeter precision using steps of 50 μm. The system is designed to deliver a maximum dose rate of 40 Gy/ min.These irradiators are operated under a common small animal irradiation facility that accepts campus wide preclinical projects. We will conclude our presentation by presenting examples of ongoing radiobiological projects that will allow us to illustrate the performance and operation of both irradiators.

Acoustic reflectivity goniometry of bounded ultrasonic pulses: Experimental verification of numerical models

The angle of incidence reflectivity of a bounded acoustic pulse from water loaded elastic solids is tested using an experimental configuration with a large transmitter and a small pointlike receiver. The experimental response, affected by well-known nonspecular effects near critical angles, is modeled fully by propagation of the full bounded pulse using a phase advance technique. This allows for visualization of the evolution of the bounded pulse with time and upon reflection. The modeled and the observed reflectivities and phase rotations, as measured along the specular path, agree well with observations even at post Rayleigh critical angles of incidence. Moreover, small amplitude deviations are accurately reproduced. The longitudinal and Rayleigh critical angles are obtained from the observed reflectivity curves and used to calculate the material elastic wave speeds, which are in good agreement with those measured directly. The density is also obtained by inversion of portions of the reflectivity curves where they do not significantly differ from the plane wave response. These tests validate use of the full phase propagation method to study such reflection problems.

A Practical Protocol to Measure Common Carotid Artery Intima-media Thickness

OBJECTIVETo describe and test a practical protocol to measure common carotid intima-media thickness that uses the combined values of two longitudinal examination angles to increase sensitivity.METHODBetween February and September 2005, 206 patients underwent duplex scan examination of carotid vessels, and the intima-media thickness of 407 common carotids were measured in three angles: transversal, longitudinal posterolateral, and anterolateral, with three intima-media thickness measurements for each near and far wall. In addition to numbers obtained from the three angles of measurement, a fourth visual perspective was obtained by combining the intima-media thickness results of posterolateral and anterolateral longitudinal views and considering the thickest wall measurement.RESULTSTwo hundred seventy (66.3%) carotid arteries had an intima-media thickness thicker than 1mm. The mean intima-media thickness values achieved by the different incidences were 1.26±0.6mm (transversal), 1.17±0.54mm (longitudinal anterolateral), and 1.18±0.58mm (longitudinal posterolateral). A significant difference in intima-media thickness measurement values was observed when the three angles of examination plus the combined positive results of both longitudinal angles were compared by ANOVA (P=0.005). The LSD Post-Hoc test determined that the combined longitudinal view results were similar to the transversal views (P=0.28) and had greater intima-media thickness means than isolated anterolateral or posterolateral longitudinal views (P=0.02 and 0.05, respectively).CONCLUSIONSThe protocol presented is a practical method for obtaining common carotid artery intima-media thickness measurements. The combined longitudinal posterolateral and anterolateral longitudinal views provide a more sensitive evaluation of the inner layers of the carotid walls than isolated longitudinal views.

Vibration analysis for elastic multi‐beam structures by the C0‐continuous time‐stepping finite element method

AbstractSome C0‐continuous time‐stepping finite element method is proposed for investigating vibration analysis of elastic multi‐beam structures. In the time direction, the C0‐continuous Galerkin method is used to discretize the generalized displacement field. In the space directions, the longitudinal displacements and rotational angles on beams are discretized using conforming linear elements, while the transverse displacements on beams are discretized by the Hermite elements of third order. The error of the method in the energy norm is proved to be O(h+k3), where h and k denote the mesh sizes of the subdivisions in the space and time directions, respectively. The finite difference analysis in time is developed to discuss the spectral behavior of the algorithms as well as their dissipation and dispersion properties in the low‐frequency regime. The method has also been extended to study some nonlinear problems. A number of numerical tests are included to illustrate the computational performance of the method. Copyright © 2008 John Wiley &amp; Sons, Ltd.

Energy decay rate of the thermoelastic Bresse system

In this paper, we study the energy decay rate for the thermoelastic Bresse system which describes the motion of a linear planar, shearable thermoelastic beam. If the longitudinal motion and heat transfer are neglected, this model reduces to the well-known thermoelastic Timoshenko beam equations. The system consists of three wave equations and two heat equations coupled in certain pattern. The two wave equations about the longitudinal displacement and shear angle displacement are effectively damped by the dissipation from the two heat equations. Actually, the corresponding energy decays exponentially like the classical one-dimensional thermoelastic system. However, the third wave equation about the vertical displacement is only weakly damped. Thus the decay rate of the energy of the overall system is still unknown. We will show that the exponentially decay rate is preserved when the wave speed of the vertical displacement coincides with the wave speed of longitudinal displacement or of the shear angle displacement. Otherwise, only a polynomial type decay rate can be obtained. These results are proved by verifying the frequency domain conditions.

THE MINIPTERIONAL CRANIOTOMY

To describe a modification of the pterional approach (PT), the minipterional craniotomy (MPT), and compare the anatomic exposure provided by these two approaches. The anatomic exposure offered by the MPT and PT were compared in eight sides of cadaver heads using a computerized tracking system, a robotic microscope, and an image-guidance system. The area of surgical exposure, angular exposure, and anatomic limits of each craniotomy were evaluated. Three recently operated clinical cases (EGF) are also reported. There were no statistical differences in the total area of surgical exposure between the two craniotomies (PT, 1524.7 +/- 305 mm; MPT, 1469.7 +/- 380.3 mm; P > 0.05) or among the ipsilateral, middle, and contralateral components of the area (P > 0.05). There were no differences in angular exposure along the longitudinal and transverse axis angles for the three selected targets, the bifurcations of internal carotid and middle cerebral arteries, and the anterior communicating artery (P > 0.05). Except for the distal portion of the operculoinsular compartment of the sylvian fissure, no significant differences in the limits of the surgical exposure through the PT and MPT were apparent on the image-guidance system. The MPT craniotomy provides comparable surgical exposure to that offered by the PT. The advantages of the MPT include reduction of tissue trauma and bony removal, a decrease in surgical time, and improved cosmetic outcomes.

X-ray diffraction patterns and anatomical properties of claw tissues of beef and dairy cattle

SUMMARYMedial claws from the right hind feet were obtained post mortem from four 19–20-month-old beef heifers and from four 28-month-old first-calving dairy heifers 3–4 days postpartum. X-ray diffraction (XRD) studies were undertaken on samples of soft and hard (cornified) integumental tissues of dorsal wall, sole and heel (bulb) for varying sites and planes of exposure. The measurements were interpreted as defining diffraction patterns and intermolecular spacings of cytoskeletal and extracellular fibrous structural proteins. The orientation of these proteins was examined in relation to physical characteristics and function including bearing of body weight by these tissues.Physical measurements taken included impression hardness which showed typically greater values for wall than sole and variable differences between horn of dairy and beef origin and husbandry systems. Claws from dairy heifers had significantly smaller values for toe (dorsal wall) angle, claw height and heel height and thickness of solear horn and heel soft tissue. Although few were studied, the results reflected typical husbandry origins and indicated the susceptibility to the lesion formation well recognized in postpartum dairy cattle.Typical XRD patterns for horn samples showed defined arcs of reflectance on the equatorial axis consistent with findings for the presence of α-helices in fibrils reported to occur in other hard-keratin-containing integumental tissues. However, reflectance on the meridional axis also reported for these other tissues was not detected. A similar defined pattern was obtained for less than 0·10 of samples of internal soft pre-cornified epidermal and attached dermal tissue although the values for intermolecular ‘d’ spacing for these were consistent with those reported for type I collagen. Diffuse reflection patterns were thus evident for the majority of samples of soft tissue epidermis and dermis and also for adipose tissue of the digital cushion.The formation of defined arcs of reflectance allowed the determination of fibril alignment in wall and solear horn. For the orientated samples of dorsal wall horn tissue, the outer layer showed a longitudinal angle of orientation essentially maintained proximal to distal. This pattern was maintained throughout the depth of horn at the proximal site. In contrast, layers in mid-wall and towards the distal edge showed a greater circumferential (horizontal) orientation in sections collected anterior to posterior towards the inner corial, including laminar, tissues. The orientation of fibrils in inner wall horn appears to relate to the direction of load-bearing forces in connecting horn to the distal phalanx. Horizontal alignment of fibrils was observed in the sole. In presenting the long axis of cells to the ground surface this orientation may facilitate erosive forces and contribute to the thinning of cornified sole horn under adverse underfoot conditions.

Anomalous quasiparticle transport and superclean superconducting state of [formula omitted

To investigate the quasiparticle dynamics in the superconducting state of quasi-two dimensional heavy fermion superconductor CeCoIn 5 , thermal conductivity tensor is measured. We obtained the quasiparticle mean free path and the density of states separately by using the combination of longitudinal thermal conductivity and thermal Hall angle. The quasiparticle mean free path increases dramatically below T c in zero magnetic field. The density of states and the scaling relation of thermal Hall conductivity are consistent with d-wave symmetry. We also argue that CeCoIn 5 is in the superclean regime. These results highlight the anomalous superconducting state in CeCoIn 5 with striking similarities with high- T c cuprates.

The craniopagus malformation: classification and implications for surgical separation

Craniopagus twins (CPT) are an uncommon, highly fascinating accident of nature. The clinical pathology of this complex entity is reviewed and placed in perspective. A logical classification aids understanding of the anomaly, and is essential to gauge outcome from separation attempts. 'Partial forms' lack significant shared dural venous sinuses (SDVS) and 'Total forms' with SDVS also exhibit more severe compressional brain distortion. Our classification consists of Partial Angular (PA), Partial Vertical (PV), Total Angular (TA) and Total Vertical (TV, formerly O'Connell Types I-III). Total vertical has a continuous cranium, and inter-twin axial facial rotation <40 degrees (Type I), 140-180 degrees (Type II) or intermediate (Type III). The term 'Angular' denotes an inter-twin longitudinal angle below 140 degrees , regardless of axial rotation. Our review categorized 64 well-delineated CPT, including 41 operative separation attempts in small children since initial success in 1952. Just over one-half were TV, almost one-third TA, and partial forms accounted for the remaining one-sixth. About 30% of CPT had shared or fused brain tissue, and a similar percentage of TA twins shared a posterior fossa. Partial forms had significantly higher birth weights, were separated at an earlier age (6 versus 11 months) and had lower mortality and better outcome compared with Total forms. A multi-staged surgical separation for Total CPT had a significantly better mortality than single-staged separation. Discussion emphasizes embryological, anatomical and clinical aspects of the malformation, with emphasis upon obstacles to a successful outcome.

Renal Anatomical Factors for the Lower Calyceal Stone Formation

The pathogenesis of urolithiasis is mainly explained with metabolic disorders. However metabolic disorders alone are not sufficient to explain this pathology. In the present study the anatomical differences in the lower calyceal stone formers were examined on both the stone forming and contralateral normal side. The objective was to assess the effect of lower pole renal anatomy on the lower calyceal stone formation. Between July 1999 and July 2004 39 patients with non-obstructed solitary lower pole stones were studied. Mean age was 47.02 years. The anatomic factors were determined on intravenous urograms (IVU). The renal length and width and the number of major and minor calices were noted. Lower pole infundibular calyceal length (ICL) and width (IW), lower infundibular length-to-width ratio were measured. The infundibulo-ureteropelvic angle (IUPA) was measured by two methods using the angle between infundibular and ureteral axes (IUPA-1), and between infundibular and ureteropelvic axes (IUPA-2). We examined a new parameter: Renal longitudinal axis-infundibulum angle (RIA) for renal stone formation. RIA was determined between two axes, including the axis connecting the central point of the pelvis opposite the margins of inferior and superior renal sinus to midpoint of renal axis and the longitudinal renal axis (Figure 2). The data of the stone forming and non-stone forming contralateral side were compared. Statistical analysis was performed by paired-t-test. The IUPA-1 of the stone forming side was more acute than the non-stone forming side, in 77% of cases. The UIPA-2 of the stone forming side was more acute than the non-stone forming side, in 72% of cases. The differences with both methods between the stone forming and contralateral normal side were statistically significant (p < 0.05). Mean ICL of stone forming side was 30.20 mm whereas it was 25.51 mm in non-stone forming contralateral side. The difference between mean ICL values was statistically significant (p < 0.05). The mean infundibular length-to-width ratio was 8.55 +/- 3.25 on the stone forming side and 7.09 +/- 2.90 on the non-stone forming contralateral side. The difference between two groups was statistically significant (p < 0.05). The differences in RIA, infundibular width (IW), renal length, renal width and the number of major and minor calyces between stone forming and non-stone forming contralateral side were not statistically significant. Anatomical disorders of lower pole collecting system may be considered as factors contributing to stone formation. IUPA (1 and 2), ICL and ICL-to-IW ratio are significantly differing factors that might predispose to lower calyceal stone formation.

Advanced vehicle–infrastructure–driver speed profile for road departure accident prevention

In this paper, we present a new method for the calculation of the maximal authorized speed in curves where the three elements of the situation, the vehicle, the driver, and the infrastructure are taken into account. The vehicle dynamics is represented by a four-wheel model that includes longitudinal slip and side-slip angle of the vehicle. Our analysis of the driver behaviour considers his ability during deceleration, taking into account the mobilized friction, while the infrastructure characteristics introduce a precise definition of the road geometry and the maximal available friction.

Wave Propagation Analysis Considering Scattering on Grain Boundaries in Solids by Finite Element Methods

With the demand of high accuracy of defection and sizing in ultrasonic testing, numerical modeling of wave propagation needs to consider the scattering of waves among the boundaries of crystal grains. In this paper, a method is developed for automatically generating grain boundaries in finite element models. The properties of received signals in intensity and frequency spectrum by simulations are compared with those by experiments. They are in excellent agreement. This model is also applied to the numerical analysis of the wave propagation under longitudinal angle beam testing for solids with various average grain diameters. Numerical results show that a diffracted longitudinal wave can be easily measured in the case where the average grain diameter is smaller than 80 μm but it is diffcult to identify the diffracted longitudinal wave when the average grain diameter is larger than 150 μm because the diffracted waves are probably masked by the scattering waves on the grain boundaries. Moreover, numerical results also show that the crystal grain model developed in this paper provides an effective way to model wave propagation quantitatively.

Search for Simultaneous Parallel EAS Events in Long Baseline EAS Arrays with LAAS

The probabilities of observing simultaneous parallel extensive air showers (EAS) produced by nuclear fragments of cosmic ray nuclei which disintegrated in collisions with solar photons are calculated as function of longitudinal angle from the sun direction. The mean separation distances of such events are also numerically simulated by analyzing fragment trajectories of nuclei in the solar magnetic field. We report on candidates of events observed at both small and long baseline array combinations in LAAS in this paper.

Biaxial model for the incidence angle dependence of the optical efficiency of photovoltaic systems with asymmetric reflectors

The optical efficiency of concentrating solar thermal and photovoltaic systems with cylindrical geometries is asymmetrical about the optical axis. Biaxial models, based on projected incidence angles, are often used to estimate the annual performance of asymmetric concentrators. However, the use of projected angles tends to underestimate optical losses in the cover glass. In this work, a biaxial model for the incidence angle dependence of the optical efficiency, which uses the transverse projected incidence angle for determining the influence of the reflector and the real incidence angle to determine the influence of the glazing is proposed. The model gives an absolute value of the optical efficiency and it is valid for concentrating systems with translational symmetry, as well as for flat plate collectors and planar photovoltaic modules. The model is validated for a system with an east–west aligned parabolic reflector without a cover glass and it is shown that the dependence on the optical efficiency of the reflector on the longitudinal angle of incidence is negligible. The model is compared with the commonly used biaxial model and it is found that the difference is a couple of percentage points when the difference between the longitudinal projected incidence angle and the real incidence angle is large and the angle of incidence on the glass is high.

EFFECT OF LONGITUDINAL SLOPE ANGLES, VIBRATION SPEEDS AND OUTLETS FOR THE PRODUCE IN GRADING, SEPARATOR OF WHEAT SEED BY USING SPECIFIC GRAVITY SEPARATOR LOCALLY MANUFACTURE

In this study a specific gravity separator has been used in order to consider the effect of three levels of: longitudinal slop angles, vibration speeds, outlets for the produce and their effect on specific weight, productivity and seed purity. The results show the longitudinal horizontal slop angle (0) surpassed significantly in recording the greatest values for all characteristics of the study. While the second vibration speed surpassed significantly in specific weight and productivity and there were no significant effect in seed purity. in the product out lets, the first out lets achieved the highest significant specific weight and seed purity, were as the third out let surpassed in giving the highest productivity. from the interaction between the three factor we can see the interaction between (-2) longitudinal slope angle and the second vibration speed at the third out lit showed the highest productivity was opteined by the interaction between the same angle (-2) and first vibration speed at the first out lit.

Robust augmented lateral acceleration flight control design for a quasi-linear parameter-varying missile

An augmented lateral acceleration autopilot is designed for a model of a tactical missile and robust stability of the closed-loop system investigated. The tail-controlled missile in the cruciform fin configuration is modelled as a second-order quasi-linear parameter-varying system. This non-linear model is obtained from the Taylor linearized model of the horizontal motion by including explicit dependence of the aerodynamic derivatives on a state (side-slip velocity) and external parameters (longitudinal velocity and roll angle). The autopilot design is based on input-output pseudolinearization, which is a restriction of input-output feedback linearization to the set of equilibria of the non-linear model. The design makes Taylor linearization of the closed-loop system independent of the choice of equilibria. Thus, if the operating points are in the vicinity of the equilibria, then only one linear model will describe closed-loop dynamics, regardless of the rate of change in the operating points. Simulations for constant lateral acceleration demands show good tracking with fast response time. Robust autopilot design taking into account parametric stability margins for uncertainty aerodynamic derivatives is implemented using convex optimization and linear matrix inequalities.

Analysis of the Hepatic Segments on the Isotropic Multi-planar Reformatted CT Images

Purpose: We wanted to evaluate the diverse distribution and relation of the hepatic segments, as divided by the portal venous territories, on the isotropic multi-planar reformatted (MPR) CT images and we wanted to find their correlation to the intrahepatic venous structures. Materials and Methods: Fifty adult patients who underwent portal phase CT images and who had the normal liver contours at CT were included in our study. The portal phase images were obtained with a slice collimation and reconstruction interval of 1.25 mm, and they were reformatted in the coronal and sagittal planes with a slab thickness of 3 mm. For analysis of these MPR images, various terms were newly defined according to the portal venous territories (e.g., three vertical planes [right, middle and left] and one transverse plane and their plane angles, the transverse and longitudinal angles). Also, the dominant segments of the right lobe were newly divided into the S7- and S8-dominant types by comparing the transverse angles. The imaging analysis was then conducted for the following: (1) the diversity of the three vertical planes and the one transverse plane and their plane angles, (2) the proportion of the dominant segments of the right lobe and their relation with the plane angles, and (3) the correlation between the dominant segments and the intrahepatic venous structures. Results: The number of the S7- and the S8-dominant types was 21 and 29, respectively. The vertical and transverse planes were undulating and diverse according to the dominant segments as follows: the plane angles of the right vertical and middle vertical planes were more vertical in the S7-dominant type than in the S8-dominant type (p

Facet orientation in the thoracolumbar spine: three-dimensional anatomic and biomechanical analysis.

Thoracolumbar facet orientations were measured and analyzed. To establish a comprehensive database for facet orientation in the thoracolumbar vertebrae and to determine the normal human condition. Most studies on facet orientation have based their conclusions on two-dimensional measurements, in small samples or isolated vertebrae. The amount of normal asymmetry in facet orientation is poorly addressed. Transverse and longitudinal facet angles were measured directly from 240 human vertebral columns (males/females, blacks/whites). The specimens' osteologic material is part of the Hamann-Todd Osteological Collection housed at the Cleveland Museum of Natural History (Cleveland, OH). A total of 4,080 vertebrae (T1-L5) from the vertebral columns of individuals 20 to 80 years of age were measured, using a Microscribe three-dimensional apparatus (Immersion Co., San Jose, CA). Data were recorded directly on computer software. Statistical analysis included paired t tests and analysis of variance. RESULTS.: Facet orientation is independent of gender, age, and ethnic group. Asymmetry in facet orientation is found in the thorax. All thoracolumbar facets are positioned in an oblique plane. In the transverse plane, all facets from T1 to T11 are positioned with an anterior inclination of approximately 25 degrees to 30 degrees from the frontal plane. The facets of T12-L2 are oriented closer to the midsagittal plane of the vertebral body (mean range, 25.89 degrees-33.87 degrees), while the facets of L3-L5 are oriented away from that plane (mean range, 40.40 degrees-56.30 degrees). Facet transverse orientation at the thoracolumbar junction is highly variable (approximately 80% with approximately 101 degrees and approximately 20% with 35 degrees). All facets are oriented more vertically from T1 (approximately 150 degrees) to L5 (approximately 170 degrees). The facet sagittal orientations of the lumbar zygoapophyseal joints are not equivalent. CONCLUSIONS.: Asymmetry in facet orientation is a normal characteristic in the thorax.