Finite element analysis of sagittal balance in different morphotype: Forces and resulting strain in pelvis and spine

In humans, vertical posture acquisition caused several changes in bones and muscles which can be assumed as verticalization. Pelvis, femur, and vertebral column gain an extension position which decreases muscular work by paravertebral muscles in the latter. It's widely known that six different morphological categories exist; each category differs from the others by pelvic parameters and vertebral column curvatures. Both values depend on the Pelvic Incidence, calculated as the angle between the axes passing through the rotation centre of the two femur heads and the vertical axis passing through the superior plate of the sacrum. The aim of this study is to evaluate the distribution of stress and the resulting strain along the axial skeleton using finite element analysis. The use of this computational method allows performing different analyses investigating how different bony geometries and skeletal structures can behavior under specific loading conditions. A computerized tomography (CT) of artificial bones, carried on at 1.5 mm of distance along sagittal, coronal and axial planes with the knee at 0° flexion (accuracy 0.5 mm), was used to obtain geometrical data of the model developed. Lines were imported into a commercial code (Hypermesh by Altair®) in order to interpolate main surfaces and create the solid version of the model. In particular six different models were created according Roussoly's classification, by arranging geometrical position of the skeletal components. Loading conditions were obtained by applying muscular forces components to T1 till to L5, according to a reference model (Daniel M. 2011), and a fixed constrain was imposed on the lower part of the femurs. Materials were assumed as elastic with an Elastic modulus of 15 GPa, a Shear Modulus of 7 GPa for bony parts, and an Elastic modulus of 6 MPa, a Shear Modulus of 3 MPa for cartilaginous parts. Six different simulations have been carried out in order to evaluate the mechanical behavior of the human vertebral column arranged according to the Russoly's classification; results confirm higher solicitations obtained varying configurations from case I to case VI. In particular way, first three cases seem to supply the different loading configurations spreading stresses in almost all the bony parts of the column, while the remaining others three cases produce an higher concentration of stress around the lower part of spine (L3, L4, L5). Results confirm a good agreement with those present in literature (Winkle et al., 1999), an equivalent Von Mises average stress was of 0,55 MPa was found on the intervertebral disks with the higher values reached on the lower part of the column. A comparison of results obtained for Case I with literature (Galbusera et al., and El Rich et al., 2004), shows a good agreement in terms of normal compressive force, while more evident differences with Galbusera's results can be found for shear force and sagittal moment. The results underline a relationship between PI increase, and accordingly of PT and LL, and the distribution of load forces. Load forcesi is exerted mainly on distal vertebrae, especially on L4 and L5.