[01] Francisco Casesnoves, Computational Bioengineering, International Institute of Informatics and Systemics, Orlando, Florida State, USA.

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.

Lumbar Artificial Implants, Reuleaux Method (RM), Numerical Reuleaux Method (NRM), Contact Mechanics, Instantaneous Rotation Center (IRC), Optimization, Numerical-Geometrical Methods

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SIAM Conference in Computational Science/Engineering. MI. USA. 2009. [05] Casesnoves, F. ´Theory and Primary Computational Simulations of the Numerical Reuleaux Method (NRM)´ International Journal of Mathematics and Computation (http://www.ceser.in/ceserp/index.php/ijmc/issue/view/119). Volume 13, Issue Number D11.2011. [06] Casesnoves, F. 'Applied Inverse Methods for Deformable Solid Dynamics/Kinematics in Numerical Reuleaux Method (NRM)' Casesnoves, F. International Journal of Numerical Methods and Applications. Volume 9(2) 2013 .Pages 109-131. Peer-Reviewed International Mathematical/Computation Journal Article Print/Online.http://www.pphmj.com/abstract/7688.htm. [07] Bartholomew-Biggs, M. Nonlinear Optimization with Engineering Applications. Springer Optimization and its Applications. 2008. [08] Casesnoves, F. Bioengineering Inverse Methods for Optimal Geometrical/Mechanical Deformation of Lumbar Artificial Disks/Implants Using the Numerical Reuleaux Method. 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