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This thesis was submitted for the degree of Doctor of Philosophy and awarded by Brunel University. The spinal column as a static structure is analysed in an attempt to quantify the mechanics of the system, of particular interest has been the derivation of forces, in operation in the muscles, required to maintain the equilibrium of the spine it various positions. Three approaches to the solution of the structural problem have been used, namely: (a) Establishing the equations of equilibrium for the thoracic and lumbar vertebrae, involving body weight, external dead load, muscle force and the intervertebral reactions. These equations are solved using the Linear Programming technique which minimizes the total force in the system. The solution gives numeric values for the muscle forces and intervertebral reactions; (b) An iteration technique, which derives the material properties of a structure from displacement and applied load data, is used to analyse simple element structures involving bars and beams; (c) Using both the Linear Programming technique and a structural analysis of the spine involving bar and beam finite elements to form a complete static model of the spine. The Linear Programming as in (a) is used in an initial upright position. The structural analysis is used to calculate the vertebral forces required to deform the spine to a deflected position. Combining the two studies gives values for the intervertebral reactions in the deformed position, these, the body weight and the dead load are input into a modified set of equations of equilibrium which are solved by Linear Programming. The method (a) has been used to give results for forward flexion, lateral flexion and a scoliotic curve with several orthopaedic supports. The approach (c) has been used for forward flexion alone. |
