- Email: [email protected]
P034 Influence of lumbar spine curvature on stress distribution in intervertebral discs
INFLUENCE OF LUMBAR SPINE CURVATURE ON STRESS DISTRIBUTION IN INTERVERTEBRAL DISCS A.Rohlmann, Th.Zander, JCahsse, GBergmann Free University Berlin, Oskar-Helene-Heim. Berlin, Germany
TO THE QUESTION OF THE FORMATION OF THE SPINAL COLUMN IN CASE OF SCOLIOSIS I. Axenovich, private doctor
INTRODUCTION: The curvature of the lumbar spine varies from patient to patient. The aim of this study was to determine the effect of different degrees of lumbar spine curvature in sagittal and frontal plane on stress distribution in intervertebral discs, MATERIALS AND METHODS: A geometrically simplified three-dimensional nonlinear finite element model of the lumbar spine with an internal spinal fixation device was used. The model consists of about 2300 elements @-node-bricks, beams, bars) and 3000 nodal points. The mechanical behaviour of the ligaments were chosen from the literature’~*. In a preceding study the muscle forces had been varied until nearly the same implant loads were calculated as measured in viva with instrumented fixators”“. These muscle forces were used in the following calculations. Five different curvatures in the sagittal and five curvatures in the frontal plane were studied. The angle between vertebral end-plates and the horizontal line in the sagittal plane for the normal curvature were multiplied by the factors 0 (straight spine), 0.5 (slightly bent spine), I.5 (strongly bent spine), and 2 (very strongly bent spine). In the frontal plane the angle between upper Ll vertebral end-plate and horizontal line was varied between 0” and 20” in 5” steps. For each spine curvature uniform angles were chosen at all levels. In all cases studied the spine was loaded as during standing. RESULTS: Spinal
curvature
only
in the sagittal
plane:
Bending moments and axial force in the tixators increased with increasing curvature. As expected, the stresses in the bridged intervertebral discs were lower than in the adjacent discs. In the L1/2 disc, the highest stresses in annulus fibrosis occurred in the mid-sagittal plane for a straight spine, but on the dorsal side for the very strongly bent spine. In the W/4 disc, the highest stresses were found on the dorsal side for a straight spine and on the ventral side for the very strongly bent spine. Spid
curvuture
only
in the frontd
In addition we have examined one-dimensioned model of the spinal column in the form of a spatial axis composed of the flexible element following one after the other (disks among the vertebrae) and the totally hard ones (vertebrae). With the model we can take into consideration external burden of the spinal column (as a result of the muscles and the weight) as well as conditions of fixing from the direction of the pelvis and the head. RESULTS AND DISCUSSION From the study we can see that in the beginning the torsion (the degree of the inclination from the flat forms) seems to be progressive increasing when learning its own plane and then beginning from the point where spine’s formation shows significant degree, the torsion decreases since the spinal column’s axis strives to lie down on the horizontal plane. The research with the mathematical model can prove the hypothesis that on the basis of the initial scoliotic deformation of the spinal column originated as a result of loss of its solidity it can be stated that the inclination of the spine may occur and result in a progressive torsion because of and depending on the spinal column’s characteristics - length. burden etc.
plane:
For a straight spine the stress distribution was symmetrically to the sagittal plane. With increasing spinal curvature, bending moments in the fixators increased on the side to which the spine was bent (ipsilateral) and decreased on the other side (contralateral). For the axial compressive force the opposite was found. The stresses in the bridged intervertebral discs were again smaller than in the adjacent discs. In the L1/2 disc, high stresses were predicted on the contralateral side of the annulus fibrosis for a strong spinal curvature. In the LA/5 disc, higher stresses were found on the ipsilateral side than on the contralateral side. DISCUSSION: The curvature of the lumbar spine has a marked influence on stress distribution in intervertebral discs. In our model we assumed healthy discs. Therefore, the stresses in the nucleus pulposes were constant. REFERENCES: 1. Gael et al., Spine, 20, 689-698, 1995. 2. Shirazi-Ad1 et al., J. Biomech., 19. 331-350. 1986. 3. Calisse, Thesis, Techn. Univ. Berlin, 1997. 4. Rohlmann et al., J. Biomech., 27, 961- 967, 1994. 5. Rohlmann et al., Spine, 20. 2683-2689. 1995. CORRESPONDENCE: Dr.-Ing. A. Rohlmann. Oskar-Helene-Heim. Clayallee 229, D-14195 Berlin, Germany Tel: (int) 49 30 81004 274; Fax: (int) 49 30 81004 275; [email protected]
72
INTRODUCTION In the study we review possibility of the origin and growth of scoliosis in consequence of mechanical instability. The statements can be proved by mathematical modelling, test problem calculations by the method of the differential geometry and clinical cases. MATERIALS AND METHODS In the study we used the calculating methods of the differential geometry, with the use of the spondilogram in two projections we have worded out the method necessary for the definition of the description of the scoliotic spinal column’s axis, the torsion (the degree of the bend of the line from the flat forms) and the pitch tangential to the curve.
I I”’ Conference
of the ESB, July
During the calculations solidity corresponding scoliosis.
we have obtained the forms of the loss of the with the C-shaped, S-shaped and complicated
In the study we can complicate further or simplify the model in order to prove the possible on-in and the development of the scoliosis depending on its biomechanical type. CORRESPONDENCE Dr. Igor Axenovich Jo6 Jbnos, Eger 3300, Hungary Tel: 00-36-36-3 lo-542
8-1 I 98, Toulouse.
France
TO THE QUESTION OF THE FORMATION OF THE SPINAL COLUMN IN CASE OF SCOLIOSIS I. Axenovich, private doctor
INTRODUCTION: The curvature of the lumbar spine varies from patient to patient. The aim of this study was to determine the effect of different degrees of lumbar spine curvature in sagittal and frontal plane on stress distribution in intervertebral discs, MATERIALS AND METHODS: A geometrically simplified three-dimensional nonlinear finite element model of the lumbar spine with an internal spinal fixation device was used. The model consists of about 2300 elements @-node-bricks, beams, bars) and 3000 nodal points. The mechanical behaviour of the ligaments were chosen from the literature’~*. In a preceding study the muscle forces had been varied until nearly the same implant loads were calculated as measured in viva with instrumented fixators”“. These muscle forces were used in the following calculations. Five different curvatures in the sagittal and five curvatures in the frontal plane were studied. The angle between vertebral end-plates and the horizontal line in the sagittal plane for the normal curvature were multiplied by the factors 0 (straight spine), 0.5 (slightly bent spine), I.5 (strongly bent spine), and 2 (very strongly bent spine). In the frontal plane the angle between upper Ll vertebral end-plate and horizontal line was varied between 0” and 20” in 5” steps. For each spine curvature uniform angles were chosen at all levels. In all cases studied the spine was loaded as during standing. RESULTS: Spinal
curvature
only
in the sagittal
plane:
Bending moments and axial force in the tixators increased with increasing curvature. As expected, the stresses in the bridged intervertebral discs were lower than in the adjacent discs. In the L1/2 disc, the highest stresses in annulus fibrosis occurred in the mid-sagittal plane for a straight spine, but on the dorsal side for the very strongly bent spine. In the W/4 disc, the highest stresses were found on the dorsal side for a straight spine and on the ventral side for the very strongly bent spine. Spid
curvuture
only
in the frontd
In addition we have examined one-dimensioned model of the spinal column in the form of a spatial axis composed of the flexible element following one after the other (disks among the vertebrae) and the totally hard ones (vertebrae). With the model we can take into consideration external burden of the spinal column (as a result of the muscles and the weight) as well as conditions of fixing from the direction of the pelvis and the head. RESULTS AND DISCUSSION From the study we can see that in the beginning the torsion (the degree of the inclination from the flat forms) seems to be progressive increasing when learning its own plane and then beginning from the point where spine’s formation shows significant degree, the torsion decreases since the spinal column’s axis strives to lie down on the horizontal plane. The research with the mathematical model can prove the hypothesis that on the basis of the initial scoliotic deformation of the spinal column originated as a result of loss of its solidity it can be stated that the inclination of the spine may occur and result in a progressive torsion because of and depending on the spinal column’s characteristics - length. burden etc.
plane:
For a straight spine the stress distribution was symmetrically to the sagittal plane. With increasing spinal curvature, bending moments in the fixators increased on the side to which the spine was bent (ipsilateral) and decreased on the other side (contralateral). For the axial compressive force the opposite was found. The stresses in the bridged intervertebral discs were again smaller than in the adjacent discs. In the L1/2 disc, high stresses were predicted on the contralateral side of the annulus fibrosis for a strong spinal curvature. In the LA/5 disc, higher stresses were found on the ipsilateral side than on the contralateral side. DISCUSSION: The curvature of the lumbar spine has a marked influence on stress distribution in intervertebral discs. In our model we assumed healthy discs. Therefore, the stresses in the nucleus pulposes were constant. REFERENCES: 1. Gael et al., Spine, 20, 689-698, 1995. 2. Shirazi-Ad1 et al., J. Biomech., 19. 331-350. 1986. 3. Calisse, Thesis, Techn. Univ. Berlin, 1997. 4. Rohlmann et al., J. Biomech., 27, 961- 967, 1994. 5. Rohlmann et al., Spine, 20. 2683-2689. 1995. CORRESPONDENCE: Dr.-Ing. A. Rohlmann. Oskar-Helene-Heim. Clayallee 229, D-14195 Berlin, Germany Tel: (int) 49 30 81004 274; Fax: (int) 49 30 81004 275; [email protected]
72
INTRODUCTION In the study we review possibility of the origin and growth of scoliosis in consequence of mechanical instability. The statements can be proved by mathematical modelling, test problem calculations by the method of the differential geometry and clinical cases. MATERIALS AND METHODS In the study we used the calculating methods of the differential geometry, with the use of the spondilogram in two projections we have worded out the method necessary for the definition of the description of the scoliotic spinal column’s axis, the torsion (the degree of the bend of the line from the flat forms) and the pitch tangential to the curve.
I I”’ Conference
of the ESB, July
During the calculations solidity corresponding scoliosis.
we have obtained the forms of the loss of the with the C-shaped, S-shaped and complicated
In the study we can complicate further or simplify the model in order to prove the possible on-in and the development of the scoliosis depending on its biomechanical type. CORRESPONDENCE Dr. Igor Axenovich Jo6 Jbnos, Eger 3300, Hungary Tel: 00-36-36-3 lo-542
8-1 I 98, Toulouse.
France