Poisson meets Escher

Abstract

Since the beginning of time, humans have been trying to replace the skeletal system in cases of trauma or disease. Medical devices were designed, manufactured, and implanted, to restore the function of the skeletal system. Fast forward to today and joint replacements are among the most common surgeries carried out in the world. Despite their success, a relatively large number of patients will eventually need a revision surgery. In most cases, the implant fails due to aseptic loosening. Aseptic loosening represents a range of implant loosening cases not associated with infection and is often linked to an inflammatory response. This kind of implant loosening is often associated with the mechanical failure of the load-bearing connection at the bone-implant interface, which could be caused by inadequate initial fixation, the loss of fixation over time, or bone tissue deterioration as a result of (wear) particles. The complexity of the bony tissue, with its hierarchical and anisotropic structure, complicates the development of life-lasting replacements.
Metallic biomaterials have been introduced as promising bone substitutes but their stiffness is usually vastly higher than that of the native bone. As a result, the patient’s bone becomes shielded from mechanical stimuli (stress shielding). Prolonged reduction in the mechanical stimuli results in bone resorption and may cause implant loosening. With the introduction of additively manufactured (AM) porous structures, the mechanical properties of metallic biomaterials could be reduced to the level of the bony tissue. Additionally, porous biomaterials allow for the diffusion of nutrients and oxygen, the ingrowth of de novo bone tissue, and the formation of capillaries. While this may sound as the golden combination, close bone-implant contact is of critical importance and can only be guaranteed if the implant matches the patient’s anatomy. Recent advances in AM have enabled the development of patient-specific implants, but this does not necessarily guarantee a lasting fixation. In the most ideal situation, the geometry of the implant should be tailored at both micro- and macroscale to optimize both shape-matching and material properties of the porous structures. This often calls for an unusual set of properties and functionalities that are not usually found in nature. Materials of which the small-scale architecture can be designed to obtain certain mechanical, mass-transport, and biological properties are referred to as meta-biomaterials.
The deformation of a material in directions perpendicular to the direction of loading is described by the Poisson’s ratio. A negative value would indicate that the material exhibits lateral expansion in response to axial tension, which can be observed in auxetic materials. This Poisson effect is usually guided by the internal structure of the material, or the micro-architecture of meta-biomaterials. Changing the building block (i.e., the unit cell) will, therefore, change the micro-architecture and, thus, the deformation behavior of the material as a whole...