Applied Inverse Methods for Optimal Deformation of Lumbar Artificial Disk/Implants with Numerical Reuleaux Method and 3D Voxelization-Computational Simulations

Lumbar artificial implants/disks experiment material deformations during the biomechanical loads/movements that are acting dynamically on the lumbar spine, e.g., flexion, extension, lateral flexion and torsion. During this biomechanical process disks and vertebras, (each spine part as a whole in general) move around an Instantaneous Rotation Center (IRC, 3D) or an Instantaneous Axis of Rotation (IAR, 2D). During extreme conditions of physical effort, the angles of IRC/IAR are enforced until reaching the maximum of their anatomical-physiological capabilities, with additional work-load for muscles, tendons, cartilage, and surrounding tissues. We carried out geometrical-mathematical-approaches to determine optimal deformation, given a selected IRC/IAR, which was chosen different from the non-deformed solid IRC/IAR, and find out the implant physical-geometrical variables linked to that obtained deformation. Voxelization of the implant in 3D constitutes the basis of this new contribution. Computational-Numerical Method was the inverse geometrical algorithms of Numerical Reuleaux Method (NRM), based on previous publications/algorithms. Once the optimal deformation was determined, the numerical 3D fitting to a nonlinear polynomial for the stress and strain was calculated. Initial results agreed to formal NRM with useful data of contact mechanics stress/strain equations/parameters and distribution/magnitudes, all complemented with matrix algebra numerical formulation and radiological experimental data. Bioengineering applications and Radiology-geometrical results, both for manufacturing design and clinical improvements were presented.