Application of Engineered Porosity and Modified Effective Moduli to the Design of Orthopaedic Implants

Commercially available orthopaedic implants have a bending stiffness (flexural rigidity) that is at least 10 times greater than cortical bone. Effects of this stiffness mismatch have been extensively studied relative to total hip arthroplasty (THA). Clinical experience with THA has shown that stiffness mismatch is the primary cause of accelerated bone resorption due to the stress shielding, resulting in sub-optimal bone loading, aseptic loosening and inadequate bone support for a future revision implant. Attempts to incorporate design features that reduce the flexural rigidity of implants have yielded inconsistent results or failures due to biomaterial incompatibilities and practical manufacturing complications. The recent development of additive manufacturing (AM) processes allow the fabrication of closed-cell porous Ti or CoCr microstructures as a practical means of fabrication while reducing implant stiffness. The use of engineered porosity to modify flexural rigidity requires an ability to predict moduli from microstructural parameters. The literature is replete with different formulas which are often contradictory; existing equations relating porosity to effective moduli are generally interpretive and not predictive. This study applied finite element methods to three-dimensional porous structures with different arrangements of spheroidal voids. The resulting data show that the effective Young\u27s modulus varies linearly with &psi, the ratio of pore radius to center-to-center dimension, for a porosity range of 20 to 50%. In addition, the arrangement of spherical voids was found to have only a minimal effect on the resultant Young\u27s modulus. Predictive equations for Poisson\u27s ratio are second-order and dependent upon the void arrangement. The effect of changes in loading direction on moduli indicate that the three microstructures evaluated in this study are anisotropic, with anisotropy increasing with both ψ and volume porosity. The predictive equations developed in this study were validated with AM fabrication and testing of prototypical Ti6Al4V spinal rods. Constructs of a rhombohedral (FCC) pore arrangement with 30% porosity showed an effective reduction of ~ 50% in Young\u27s modulus. Predicted values for flexural rigidity fell within 95% confidence intervals for the tested porous Ti6Al4V constructs, confirming a design methodology with the potential of reducing the flexural rigidity, and resulting bone resorption, of orthopaedic implants

Young’s Modulus and Volume Porosity Relationships for Additive Manufacturing Applications

Recent advancements in additive manufacturing (or rapid prototyping) technologies allow the fabrication of end-use components with defined porous structures. For example, one area of particular interest is the potential to modify the flexibility (bending stiffness) of orthopedic implants through the use of engineered porosity (i.e., design and placement of pores) and subsequent fabrication of the implant using additive manufacturing processes. However, applications of engineered porosity require the ability to accurately predict mechanical properties from knowledge or characterization of the pore structure and the existence of robust equations characterizing the property–porosity relationships. As Young’s modulus can be altered by variations in pore shape as well as pore distribution, numerous semi-analytical and theoretical relationships have been proposed to describe the dependence of mechanical properties on porosity. However, the utility and physical meaning of many of these relationships is often unclear as most theoretical models are based on some idealized physical microstructure, and the resulting correlations often cannot be applied to real materials and practical applications. This review summarizes the evolution and development of relationships for the effective Young’s modulus of a porous material and concludes that verifiable equations yielding consistently reproducible results tied to specific pore structures do not yet exist. Further research is needed to develop and validate predictive equations for the effective Young’s modulus over a volume porosity range of 20–50 %, the range of interest over which existing equations, whether based on effective medium theories or empirical results, demonstrate the largest disparity and offers the greatest opportunity for beneficial modification of bending stiffness in orthopedic applications using currently available additive manufacturing techniques

Young’s Modulus and Volume Porosity Relationships for Additive Manufacturing Applications

Recent advancements in additive manufacturing (or rapid prototyping) technologies allow the fabrication of end-use components with defined porous structures. For example, one area of particular interest is the potential to modify the flexibility (bending stiffness) of orthopedic implants through the use of engineered porosity (i.e., design and placement of pores) and subsequent fabrication of the implant using additive manufacturing processes. However, applications of engineered porosity require the ability to accurately predict mechanical properties from knowledge or characterization of the pore structure and the existence of robust equations characterizing the property–porosity relationships. As Young’s modulus can be altered by variations in pore shape as well as pore distribution, numerous semi-analytical and theoretical relationships have been proposed to describe the dependence of mechanical properties on porosity. However, the utility and physical meaning of many of these relationships is often unclear as most theoretical models are based on some idealized physical microstructure, and the resulting correlations often cannot be applied to real materials and practical applications. This review summarizes the evolution and development of relationships for the effective Young’s modulus of a porous material and concludes that verifiable equations yielding consistently reproducible results tied to specific pore structures do not yet exist. Further research is needed to develop and validate predictive equations for the effective Young’s modulus over a volume porosity range of 20–50 %, the range of interest over which existing equations, whether based on effective medium theories or empirical results, demonstrate the largest disparity and offers the greatest opportunity for beneficial modification of bending stiffness in orthopedic applications using currently available additive manufacturing techniques