Novel Angular Measures of Cervical Deformity Account for Upper Cervical Compensation and Sagittal Alignment

Themistocles S Protopsaltis1, Renaud Lafage, Shaleen Vira

  • 1*Department of Orthopedic Surgery, New York University Langone Hospital for Joint Diseases †Hospital for Special Surgery, Spine Service, New York, NY ‡Department of Neurosurgery, Johns Hopkins University Hospital, Baltimore, MD §Department of Surgery, University of Calgary, Calgary AB, Canada ∥Department of Orthopaedic Surgery, Pittsburg University Medical Center, Pittsburg, PA ¶Department of Neurosurgery, University of Virginia School of Medicine, Charlottesville, VA #San Diego Center for Spinal Disorders, La Jolla ††Department of Orthopedic Surgery, University of California Davis, Sacramento ‡‡Department of Neurosurgery, University of California San Francisco, San Francisco, CA **Department of Orthopedic Surgery, Oregon Health Sciences University, Portland, OR.

Abstract

Related Concept Videos

Unsymmetric Bending - Angle of Neutral Axis01:15

Unsymmetric Bending - Angle of Neutral Axis

Unsymmetrical bending occurs when a structural member is subjected to bending moments in a plane that does not align with the member's principal axes. This scenario typically arises in beams and other structural components when loads are applied at non-ideal angles, introducing complexities in stress analysis.
When a bending moment is applied at an angle θ concerning the vertical axis of a symmetrical member, it can be resolved into components along the member's principal...
927
Deformations in a Symmetric Member in Bending01:18

Deformations in a Symmetric Member in Bending

When analyzing the deformation of a symmetric prismatic member subjected to bending by equal and opposite couples, it becomes clear that as the member bends, the originally straight lines on its wider faces curve into circular arcs, with a constant radius centered at a point known as Point C. This phenomenon helps to understand the stress and strain distribution within the member more clearly.
When the member is segmented into tiny cubic elements, it is observed that the primary stress...
554
Bending of Curved Members - Strain Analysis01:14

Bending of Curved Members - Strain Analysis

The mechanics of deformation in curved members, such as beams or arches, under bending moments, involve complex responses. When such a member, symmetric about the y-axis and shaped like a segment of a circle centered at point C, is subjected to equal and opposite forces, its curvature and surface lengths change significantly. This alteration results in the shift of the curvature's center from C to C', indicating a tighter curve.
The important part of bending analysis for such a member...
560
Vertebral Column: Regions and Curvature01:16

Vertebral Column: Regions and Curvature

The vertebral column or spine is a flexible column that supports the head, neck, and body and  allows for their movements. It also protects the spinal cord.
Regions of the Vertebral Column
In an adult, the spine is subdivided into five regions: the cervical, the thoracic, the lumbar, the sacral, and the coccygeal region. The spine initially develops as a series of 33 vertebrae; after 20 years of age, the nine bones in the sacral region, five sacral, and four coccygeal bones fuse to form...
11.1K
Beams with Unsymmetric Loadings01:17

Beams with Unsymmetric Loadings

Analyzing a supported beam under unsymmetrical loadings is essential in structural engineering to understand how beams respond to varied force distributions. This analysis involves calculating the deflection and identifying points where the slope of the beam is zero, which are crucial for ensuring structural stability and functionality.
The first moment-area theorem determines the slope at any point on the beam. This theorem indicates that the change in slope between two points on a beam...
465
Unsymmetric Bending01:18

Unsymmetric Bending

Unsymmetrical bending occurs when the bending moment applied to a structural member does not align with its principal axis. This misalignment leads to complex stress distributions and deflection patterns that differ from those in symmetrical bending, and are essential for designing structures to withstand different loading conditions. In unsymmetrical bending, the neutral axis—where stress is zero—does not necessarily align with the geometric axes of the cross-section. The...
886