Do Alterations in Vertebral and Disc Dimensions Affect an Elliptical Model of the Thoracic Kyphosis?
Do Alterations in Vertebral and Disc Dimensions Affect an Elliptical Model of the Thoracic Kyphosis?
Authors
- Donald D. Harrison, PhD, DC, MSE
- Deed E. Harrison, DEC
- Tadeusz J. Janik, PhD
- Rene Cailliet, MD
- Jason Haas, DC
Publication
SPINE 2003; 28(5): 463-469.
Article Link
Do Alterations in Vertebral and Disc Dimensions Affect an Elliptical Model of the Thoracic Kyphosis?
Abstract
Study Design. Mathematical modeling, using least squares method, of thoracic kyphosis was constructed as digitized points from radiographs of 50 healthy patients.
Objective. To determine a simple geometric model of the thoracic kyphosis.
Summary of Background Data. Thoracic kyphosis is an important parameter of health, but geometric models of kyphosis are rare. Few papers report vertebral body and disc height data.
Methods. Thoracic vertebral bodies were digitized on lateral radiographs of 50 healthy patients. The average path of the posterior vertebral body corners of T1 through T12 was modeled, in the least squares sense, with a portion of an ellipse. The best-fit ellipse was sectioned with different model partitions using four sets of vertebral body heights and disc heights. Segmental and global angles derived from these four models were compared with reported values in the literature.
Results. A 72° portion of an ellipse, with a minor-to-major axis ratio of 0.69, can closely approximate the path of the posterior body corners from the inferior of T1 to the superior of T12. The posterior vertebral body heights and disc heights have an average ratio of approximately 5:1. Segmental angles from T3-T4 through T11-T12 for all four models are close to other reported values. The thoracic spine has a height-to-length ratio of approximately 0.96.
Conclusions. Thoracic kyphosis from inferior-posterior T1 to superior-posterior T12 can be closely modeled (least squares error per point , 1 mm) with a 72° piece of an ellipse with a minor-to-major axis ratio of 0.69. The major axis is parallel to the posterior body margin of T12, whereas the minor axis passes through the superior end- plate of T12. Segmental angles derived from this elliptical modeling are in the range of values from healthy patients.
- Donald D. Harrison, PhD, DC, MSE
- Deed E. Harrison, DEC
- Tadeusz J. Janik, PhD
- Rene Cailliet, MD
- Jason Haas, DC
SPINE 2003; 28(5): 463-469.
Do Alterations in Vertebral and Disc Dimensions Affect an Elliptical Model of the Thoracic Kyphosis?
Study Design. Mathematical modeling, using least squares method, of thoracic kyphosis was constructed as digitized points from radiographs of 50 healthy patients.
Objective. To determine a simple geometric model of the thoracic kyphosis.
Summary of Background Data. Thoracic kyphosis is an important parameter of health, but geometric models of kyphosis are rare. Few papers report vertebral body and disc height data.
Methods. Thoracic vertebral bodies were digitized on lateral radiographs of 50 healthy patients. The average path of the posterior vertebral body corners of T1 through T12 was modeled, in the least squares sense, with a portion of an ellipse. The best-fit ellipse was sectioned with different model partitions using four sets of vertebral body heights and disc heights. Segmental and global angles derived from these four models were compared with reported values in the literature.
Results. A 72° portion of an ellipse, with a minor-to-major axis ratio of 0.69, can closely approximate the path of the posterior body corners from the inferior of T1 to the superior of T12. The posterior vertebral body heights and disc heights have an average ratio of approximately 5:1. Segmental angles from T3-T4 through T11-T12 for all four models are close to other reported values. The thoracic spine has a height-to-length ratio of approximately 0.96.
Conclusions. Thoracic kyphosis from inferior-posterior T1 to superior-posterior T12 can be closely modeled (least squares error per point , 1 mm) with a 72° piece of an ellipse with a minor-to-major axis ratio of 0.69. The major axis is parallel to the posterior body margin of T12, whereas the minor axis passes through the superior end- plate of T12. Segmental angles derived from this elliptical modeling are in the range of values from healthy patients.
