Mathematical and Finite Element Modelling of Spine to Investigate the Effects of Intra-Abdominal Pressure and Activation of Muscles Around Abdomen on the Spinal Stability

Abstract

In spite of the several experimental and modeling studies on the biomechanical characteristics of the human spine, the role and significance of the intra-abdominal pressure (IAP) in spine mechanics has remained controversial. This study represents a simple analytical and a 3-D finite element model of spine and its surrounding structures to investigate the contribution of IAP to spinal stability. The mathematical model included the lumbar spine column, the abdominal cavity and a muscular layer around it, the rib cage and the pelvic ring. The lumbar spine column was modeled as a beam and the rib cage and pelvis as rigid bodies. The intra-abdominal cavity and the surrounding muscular layer were represented by a thin-wall cylindrical vessel with deformable shell wall. The free body diagram and equilibrium equations of each body of the model were derived while an external load to the rib cage was applied. The equations were then combined with the force-deflection relationships for the beam bending, the IAP fluid volume variation, and the muscle shell traction. Muscle activation levels were simulated by changing the Young’s modulus of the shell in the direction of fibers, up to an upper-limit value which was obtained based on the Valsalva maneuver. In the Finite Element (FE) model, the abdominal cavity was assumed to be cylindrical and filled by fluid with a bulk modulus of IMPa. The surrounding muscular layer was modeled as membrane with transverse isotropic material properties considering their fibers orientation. The spine, rib cage and pelvic ring were modeled by beam elements. The top plate simulated the active and/or passive role of diaphragm through its vertical displacement. The bottom membrane and distal spine were fully constrained. Good agreement between the analytical and FE model results was obtained. A larger external force and/or higher level of muscle activation caused a higher IAP, improving spinal unloading and stability. This effect was more significant for muscles with more horizontally directed fibers, e.g., Transverse Abdominis (TA).