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Loading response of nucleus and annulus of the human vertebra
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Abstracts
SESSION 7: BONE STRUCTURE Chairperson: J. Lawrence Katz A BIOMECHANICAL
FORMULATION
OF STRESS MODULATION
OF GROWTH
Ian A.F. Stokes, Mack Gardner-Morse, and Jeffrey P. Laible Departments of Orthopaedics and Rehabilitation, and Civil and Mechanical Engineering, University of Vermont, Burlington, Vermont 05405, USA. Forces applied to growing bone can alter its growth, but most mathematical descriptions are of remodelling of mature bone, or of ossification process. This paper examines the characteristics of a linear formulation ut’ bone growth modulated by stress. The model was tested in three analytical systems: (1) A simple fixed end cantilever beam where varying the computation step size and stress modulation factor produced stable behavior in all cases examined. (2) A 2-D, statically indeterminate model of two ribs, a vertebra and the sternum which was potentially unstable. This instability seemed to result from accumulation of stress, and an inherent instability of the model system. (3) A 3-D model of the rib cage with the lumbar and thoracic spine, with the ends of the spine redundantly constrained which also seemed to be sensitive to the stress modulation factor. To obtain stability of this hypothetical linear stress/growth interaction, it is necessary to reduce the stress modulation factor, or to introduce stress relaxation to prevent accumulation of internal stresses. LOADING RESPONSE OF NUCLEUS AND ANNULUS OF THE HUMAN VERTEBRA Harcharan Singh Ranu Dept. of Biomechanics, NYCOM, New York Institute of Technology, Old Westbury, NY 11568, USA The intradiscal and the intervertebral pressure transducers were used to measure the distribution of stresses in the nucleus and within the annulus of the human spinal disc to the point of bony fracture of the segmental units. The results show that for normal discs, the stresses developed in the nucleus and within the annulus are linearly related to each other and to the compressive load. Strains developed around the periphery of the vertebral body are also linear with the compressive loads; when the partial vertebral column is loaded to the point of bony fracture. An important finding was that, at the point of fracture with maximum stress in normal discs, there was no failure of the annulus fibrosus and no extrusion of the nucleus. althouah at the point of fracture bone marrow oozed out of the endplates of the vertebral bodies and there was a cracking noise at the moment of yielding. Blood was also discharged from the vertebral body surface pores at this time. Therefore, it can be assumed that a change occurs in the structure of the spinal disc of older persons which permits relatively minor compressive stresses to cause disc herniation. THREE DIMENSIONAL DISTRIBUTION OF TRABECULAR CENTRUM
BONE IN THE LUMBAR VERTEBRAL
J.A. Main3, T.S. Keller’*2~3, D.M. Spengler’, A.M. Strauss3 ‘VA Medical Center, Nashville, TN *Dept. of Orthop. & Rehab., Vanderbilt Univ., Nashville, TN 3Dept. of Mechanical Engr., Vanderbilt Univ., Nashville, TN The nuroose of this studv was to ouantifv lumbar vertebral trabecular anatomv using direct dinitization and computed tomography (CT) images. A lumbar motion segment (Ll-L2) was p&ted & polyeste; resin, imaged with CT and sectioned at 25 mm intervals resulting in a total of 10 X-sections in the L2 centrum. The trabecular structure of each slice was dinitized and area1 bone fractions calculated from the thresholded image. Area1 bone fractions were calculated at 2347 sampling sites throughout the L2 centtum. Analysis of the data-along the coronal plane indicated a significantly lower bone fraction in the central third of the centrum as compared to the superior and inferior thirds. Differences were also noted between the superior and inferior halves of the centrum in the posterior regions, the latter being significantly greater. Analysis of the morphological anisotropy based upon the CT-derived density were consistent with the area bone fraction calculations. A TECHNIQUE FOR EVALUATING THIRD METACARPAL BONE.
SECONDARY REMODELING
IN THE DIAPHYSIS OF THE EQUINE
CM. Les, Department of Veterinary Anatomy, School of Veterinary Medicine, University of California, Davis, CA 95616: M.R. Simon. G.J. Piianowski. J.C. Eurell. Department of Veterinary Biosciences, College of Veterinary Medicine, Universiiy of Illinois, Urbana; IL 61801 A technique was established to map and evaluate the positions of secondary osteons within a bone. Assuming that the distribution of secondary osteons will provide an historical record of strain within the bone, this method could be used as an adjunct to surface strain gauge data to better understand the biomechanics of the equine metacarpus. Cross-sectional blocks from the diaphysis of pony third metacarpal bones were step-sectioned, and the positions of secondary osteons were digitized. The distribution patterns of the osteons were then analyzed against several theoretical distributions. The pattern of osteons in this bone was non-random, approaching a Markov-Polya distribution, with tendencies toward clustering. Remodeling in this bone was sparse, however, there appeared to be focal areas of heavy remodeling in the immediate vicinity of the ligaments to the second and fourth metacarpal bones, perhaps indicating a structural role for these splint bones in the biomechanics of the equine metacarpus.
Abstracts
SESSION 7: BONE STRUCTURE Chairperson: J. Lawrence Katz A BIOMECHANICAL
FORMULATION
OF STRESS MODULATION
OF GROWTH
Ian A.F. Stokes, Mack Gardner-Morse, and Jeffrey P. Laible Departments of Orthopaedics and Rehabilitation, and Civil and Mechanical Engineering, University of Vermont, Burlington, Vermont 05405, USA. Forces applied to growing bone can alter its growth, but most mathematical descriptions are of remodelling of mature bone, or of ossification process. This paper examines the characteristics of a linear formulation ut’ bone growth modulated by stress. The model was tested in three analytical systems: (1) A simple fixed end cantilever beam where varying the computation step size and stress modulation factor produced stable behavior in all cases examined. (2) A 2-D, statically indeterminate model of two ribs, a vertebra and the sternum which was potentially unstable. This instability seemed to result from accumulation of stress, and an inherent instability of the model system. (3) A 3-D model of the rib cage with the lumbar and thoracic spine, with the ends of the spine redundantly constrained which also seemed to be sensitive to the stress modulation factor. To obtain stability of this hypothetical linear stress/growth interaction, it is necessary to reduce the stress modulation factor, or to introduce stress relaxation to prevent accumulation of internal stresses. LOADING RESPONSE OF NUCLEUS AND ANNULUS OF THE HUMAN VERTEBRA Harcharan Singh Ranu Dept. of Biomechanics, NYCOM, New York Institute of Technology, Old Westbury, NY 11568, USA The intradiscal and the intervertebral pressure transducers were used to measure the distribution of stresses in the nucleus and within the annulus of the human spinal disc to the point of bony fracture of the segmental units. The results show that for normal discs, the stresses developed in the nucleus and within the annulus are linearly related to each other and to the compressive load. Strains developed around the periphery of the vertebral body are also linear with the compressive loads; when the partial vertebral column is loaded to the point of bony fracture. An important finding was that, at the point of fracture with maximum stress in normal discs, there was no failure of the annulus fibrosus and no extrusion of the nucleus. althouah at the point of fracture bone marrow oozed out of the endplates of the vertebral bodies and there was a cracking noise at the moment of yielding. Blood was also discharged from the vertebral body surface pores at this time. Therefore, it can be assumed that a change occurs in the structure of the spinal disc of older persons which permits relatively minor compressive stresses to cause disc herniation. THREE DIMENSIONAL DISTRIBUTION OF TRABECULAR CENTRUM
BONE IN THE LUMBAR VERTEBRAL
J.A. Main3, T.S. Keller’*2~3, D.M. Spengler’, A.M. Strauss3 ‘VA Medical Center, Nashville, TN *Dept. of Orthop. & Rehab., Vanderbilt Univ., Nashville, TN 3Dept. of Mechanical Engr., Vanderbilt Univ., Nashville, TN The nuroose of this studv was to ouantifv lumbar vertebral trabecular anatomv using direct dinitization and computed tomography (CT) images. A lumbar motion segment (Ll-L2) was p&ted & polyeste; resin, imaged with CT and sectioned at 25 mm intervals resulting in a total of 10 X-sections in the L2 centrum. The trabecular structure of each slice was dinitized and area1 bone fractions calculated from the thresholded image. Area1 bone fractions were calculated at 2347 sampling sites throughout the L2 centtum. Analysis of the data-along the coronal plane indicated a significantly lower bone fraction in the central third of the centrum as compared to the superior and inferior thirds. Differences were also noted between the superior and inferior halves of the centrum in the posterior regions, the latter being significantly greater. Analysis of the morphological anisotropy based upon the CT-derived density were consistent with the area bone fraction calculations. A TECHNIQUE FOR EVALUATING THIRD METACARPAL BONE.
SECONDARY REMODELING
IN THE DIAPHYSIS OF THE EQUINE
CM. Les, Department of Veterinary Anatomy, School of Veterinary Medicine, University of California, Davis, CA 95616: M.R. Simon. G.J. Piianowski. J.C. Eurell. Department of Veterinary Biosciences, College of Veterinary Medicine, Universiiy of Illinois, Urbana; IL 61801 A technique was established to map and evaluate the positions of secondary osteons within a bone. Assuming that the distribution of secondary osteons will provide an historical record of strain within the bone, this method could be used as an adjunct to surface strain gauge data to better understand the biomechanics of the equine metacarpus. Cross-sectional blocks from the diaphysis of pony third metacarpal bones were step-sectioned, and the positions of secondary osteons were digitized. The distribution patterns of the osteons were then analyzed against several theoretical distributions. The pattern of osteons in this bone was non-random, approaching a Markov-Polya distribution, with tendencies toward clustering. Remodeling in this bone was sparse, however, there appeared to be focal areas of heavy remodeling in the immediate vicinity of the ligaments to the second and fourth metacarpal bones, perhaps indicating a structural role for these splint bones in the biomechanics of the equine metacarpus.