Poisson meets Escher: Exploring the Poisson effect in bone implant design

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...Biomaterials & Tissue Biomechanic

Auxetic mechanical metamaterials

The surge of interest in so-called "designer materials" during the last few years together with recent advances in additive manufacturing (3D printing) techniques that enable fabrication of materials with arbitrarily complex nano/micro-architecture have attracted increasing attention to the concept of mechanical metamaterials. Owing to their rationally designed nano/micro-architecture, mechanical metamaterials exhibit unusual properties at the macro-scale. These unusual mechanical properties could be exploited for the development of materials with advanced functionalities, with applications in soft robotics, biomedicine, soft electronics, acoustic cloaking, etc. Auxetic mechanical metamaterials are identified by a negative Poisson's ratio and are perhaps the most widely studied type of mechanical metamaterials. Similar to other types of mechanical metamaterials, the negative Poisson's ratio of auxetics is generally a direct consequence of the topology of their nano/micro-architecture. This paper therefore focuses on the topology-property relationship in three main classes of auxetic metamaterials, namely re-entrant, chiral, and rotating (semi-) rigid structures. While the deformation mechanisms in the above-mentioned types of structures and their relationship with the large-scale mechanical properties receive most attention, the emerging concepts in design of auxetics such as the use of instability in soft matter and origami-based structures are discussed as well. Furthermore, the data available in the literature regarding the elastic properties of auxetic mechanical metamaterials are systematically analyzed to identify the spread of Young's modulus-Poisson's ratio duos achieved in the auxetic materials developed to date.Biomaterials & Tissue Biomechanic

Non-auxetic mechanical metamaterials

The concept of "mechanical metamaterials" has become increasingly popular, since their macro-scale characteristics can be designed to exhibit unusual combinations of mechanical properties on the micro-scale. The advances in additive manufacturing (AM, three-dimensional printing) techniques have boosted the fabrication of these mechanical metamaterials by facilitating a precise control over their micro-architecture. Although mechanical metamaterials with negative Poisson's ratios (i.e., auxetic metamaterials) have received much attention before and have been reviewed multiple times, no comparable review exists for architected materials with positive Poisson's ratios. Therefore, this review will focus on the topology-property relationships of non-auxetic mechanical metamaterials in general and five topological designs in particular. These include the designs based on the diamond, cube, truncated cube, rhombic dodecahedron, and the truncated cuboctahedron unit cells. We reviewed the mechanical properties and fatigue behavior of these architected materials, while considering the effects of other factors such as those of the AM process. In addition, we systematically analyzed the experimental, computational, and analytical data and solutions available in the literature for the titanium alloy Ti-6Al-4V. Compression dominated lattices, such as the (truncated) cube, showed the highest mechanical properties. All of the proposed unit cells showed a normalized fatigue strength below that of solid titanium (i.e., 40% of the yield stress), in the range of 12-36% of their yield stress. The unit cells discussed in this review could potentially be applied in bone-mimicking porous structures.Biomaterials & Tissue Biomechanic

Rationally designed meta-implants: a combination of auxetic and conventional meta-biomaterials

Rationally designed meta-biomaterials present unprecedented combinations of mechanical, mass transport, and biological properties favorable for tissue regeneration. Here we introduce hybrid meta-biomaterials with rationally-distributed values of negative (auxetic) and positive Poisson’s ratios, and use them to design meta-implants that unlike conventional implants do not retract from the bone under biomechanical loading. We rationally design and additively manufacture six different types of meta-biomaterials (three auxetic and three conventional), which then serve as the parent materials to six hybrid meta-biomaterials (with or without transitional regions). Both single and hybrid meta-biomaterials are mechanically tested to reveal their full-field strain distribution by digital image correlation. The best-performing hybrid metabiomaterials are then selected for the design of meta-implants (hip stems), which are tested under simulated-implantation conditions.Full-field strain measurements clearly show that, under biomechanical loading, hybrid meta-implants press onto the bone on both the medial and lateral sides, thereby improving implant–bone contact and potentially implant longevity.Biomaterials & Tissue Biomechanic

Merging strut-based and minimal surface meta-biomaterials: Decoupling surface area from mechanical properties

The rational design of bone-substituting biomaterials is relatively complex because they should meet a long list of requirements for optimal performance. Meta-biomaterials are micro-architected materials that hold great promise for meeting those requirements as they offer a unique combination of mechanical, mass-transport, and biological properties. There are, however, inherent couplings between the different types of properties of many such materials that make it impossible to simultaneously achieve all the design criteria. An example of such a coupling exists between the mechanical properties and the surface area. Strut-based, metallic meta-biomaterials are known to offer bone-mimicking mechanical properties, but they have limited surface area for cell adherence. Increasing the surface generally results in an undesirable increase in the mechanical properties that could lead to stress shielding. Here, we combine strut-based lattices with minimal surfaces to decouple these two properties. We added minimal surface patches to the designs of both auxetic and non-auxetic meta-biomaterials while minimizing their contribution to the mechanical properties of the resulting meta-biomaterials through the rational application of cuts or “slits”. All designs were additively manufactured using selective laser melting and mechanically tested to obtain their quasi-static mechanical properties, including their Poisson's ratio, in two configurations. A finite element-based computational homogenization code was used to compute the elastic moduli and anisotropy of the structures. The results show that the minimal surface patches substantially increase the available surface area without significantly affecting the mechanical properties. Without the slits, the surfaces significantly affected the elastic modulus and deformation behavior of the meta-biomaterials. A similar strategy could be used to tune the biodegradation rate of biodegradable metals and the permeability of meta-biomaterials in general.Biomaterials & Tissue Biomechanic

Fatigue performance of auxetic meta-biomaterials

Meta-biomaterials offer a promising route towards the development of life-lasting implants. The concept aims to achieve solutions that are ordinarily impossible, by offering a unique combination of mechanical, mass transport, and biological properties through the optimization of their small-scale geometrical and topological designs. In this study, we primarily focus on auxetic meta-biomaterials that have the extraordinary ability to expand in response to axial tension. This could potentially improve the longstanding problem of implant loosening, if their performance can be guaranteed in cyclically loaded conditions. The high-cycle fatigue performance of additively manufactured (AM) auxetic meta-biomaterials made from commercially pure titanium (CP-Ti) was therefore studied. Small variations in the geometry of the re-entrant hexagonal honeycomb unit cell and its relative density resulted in twelve different designs (relative density: ~5–45%, re-entrant angle = 10–25°, Poisson's ratio = -0.076 to -0.504). Micro-computed tomography, scanning electron microscopy and mechanical testing were used to respectively measure the morphological and quasi-static properties of the specimens before proceeding with compression-compression fatigue testing. These auxetic meta-biomaterials exhibited morphological and mechanical properties that are deemed appropriate for bone implant applications (elastic modulus = 66.3–5648 MPa, yield strength = 1.4–46.7 MPa, pore size = 1.3–2.7 mm). With an average maximum stress level of 0.47 σy at 106 cycles (range: 0.35 σyσy- 0.82 σyσy), the auxetic structures characterized here are superior to many other non-auxetic meta-biomaterials made from the same material. The optimization of the printing process and the potential application of post-processing treatments could improve their performance in cyclically loaded settings even further. Statement of Significance: Auxetic meta-biomaterials have a negative Poisson's ratio and, therefore, expand laterally in response to axial tension. Recently, they have been found to restore bone-implant contact along the lateral side of a hip stem. As a result, the bone will be compressed along both of the implant's contact lines, thereby actively reducing the risk of implant failure. In this case the material will be subjected to cyclic loading, for which no experimental data has been reported yet. Here, we present the first ever study of the fatigue performance of additively manufactured auxetic meta-biomaterials based on the re-entrant hexagonal honeycomb. These results will advance the adoption of auxetic meta-biomaterials in load-bearing applications, such as the hip stem, to potentially improve implant longevity.Biomaterials & Tissue BiomechanicsStructural Integrity & Composite

Mechanisms of fatigue crack initiation and propagation in auxetic meta-biomaterials

The fatigue performance of additively manufactured auxetic meta-biomaterials made from commercially pure titanium has been studied only recently. While certain assumptions have been made regarding the mechanisms underlying their fatigue failure, the exact mechanisms are not researched yet. Here, we studied the mechanisms of crack formation and propagation in cyclically loaded auxetic meta-biomaterials. Twelve different designs were subjected to compression-compression fatigue testing while performing full-field strain measurement using digital image correlation (DIC). The fatigue tests were stopped at different points before complete specimen failure to study the evolution of damage in the micro-architecture of the specimens using micro-computed tomography (micro-CT). Furthermore, finite element models were made to study the presence of stress concentrations. Structural weak spots were found in the inverted nodes and the vertical struts located along the outer rim of the specimens, matching the maximum principal strain concentrations and fracture sites in the DIC and micro-CT data. Cracks were often found to originate from internal void spaces or from sites susceptible to mode-I cracking. Many specimens maintained their structural integrity and exhibited no signs of rapid strain accumulation despite the presence of substantial crack growth. This observation underlines the importance of such microscale studies to identify accumulated damage that otherwise goes unnoticed. The potential release of powder particles from damaged lattices could elicit a foreign body response, adversely affecting the implant success. Finding the right failure criterion, therefore, requires more data than only those pertaining to macroscopic measurements and should always include damage assessment at the microscale. Statement of significance: The negative Poisson's ratio of auxetic meta-biomaterials makes them expand laterally in response to axial tension. This extraordinary property has great potential in the field of orthopedics, where it could enhance bone-implant contact. The fatigue performance of additively manufactured auxetic meta-biomaterials has only recently been studied and was found to be superior to many other bending- and stretch-dominated micro-architectures. In this study, we go beyond these macroscopic measurements and focus on the crack initiation and propagation. Full-field strain measurements and 3D imaging are used to paint a detailed picture of the mechanisms underlying fatigue. Using these data, specific aspects of the design and/or printing process can be targeted to improve the performance of auxetic meta-biomaterials in load-bearing applications.Biomaterials & Tissue BiomechanicsStructural Integrity & Composite

Additively manufactured space-filling meta-implants

The unprecedented properties of meta-biomaterials could pave the way for the development of life-lasting orthopedic implants. Here, we used non-auxetic meta-biomaterials to address the shortcomings of the current treatment options in acetabular revision surgery. Due to the severe bone deficiencies and poor bone quality, it can be very challenging to acquire adequate initial implant stability and long-term fixation. More advanced treatments, such as patient-specific implants, do guarantee the initial stability, but are formidably expensive and may eventually fail due to stress shielding. We, therefore, developed meta-implants furnished with a deformable porous outer layer. Upon implantation, this layer plastically deforms into the defects, thereby improving the initial stability and homogeneously stimulating the surrounding bone. We first studied the space-filling behavior of additively manufactured pure titanium lattices, based on six different unit cells, in a compression test complemented with full-field strain measurements. The diamond, body-centered cubic, and rhombic dodecahedron unit cells were eventually selected for the design of the deformable porous outer layer. Each design came in three different relative density profiles, namely maximum (MAX), functionally graded (FG), and minimum (MIN). After their compression in bone-mimicking molds with simulated acetabular defects, the space-filling behavior of the implants was evaluated using load-displacement curves, micro-CT images, and 3D reconstructions. The meta-implants with an FG diamond infill exhibited the most promising space-filling behavior. However, the required push-in forces exceed the impact forces currently applied in surgery. Future research should, therefore, focus on design optimization, to improve the space-filling behavior and to facilitate the implantation process for orthopedic surgeons. Statement of significance: Ideally, orthopedic implants would last for the entire lifetime of the patient. Unfortunately, they rarely do. Critically sized defects are a common sight in the revision of acetabular cups, and rather difficult to treat. The permanent deformation of lattice structures can be used to create shape-morphing implants that would fill up the defect site, and thereby restore the physiological loading conditions. Bending-dominated structures were incorporated in the porous outer layer of the space-filling meta-implants for their considerable lateral expansion in response to axial compression. A functionally graded density offered structural integrity at the joint while enhancing the deformability at the bone-implant interface. With the use of a more ductile metal, CP-Ti, these meta-implants could be deformed without strut failure.Biomaterials & Tissue Biomechanic

Mechanical performance of auxetic meta-biomaterials

The innovative design of orthopedic implants could play an important role in the development of life-lasting implants, by improving both primary and secondary implant fixations. The concept of meta-biomaterials aims to achieve a unique combination of mechanical, mass transport, and biological properties through optimized topological design of additively manufactured (AM) porous biomaterials. In this study, we primarily focused on a specific class of meta-biomaterials, namely auxetic meta-biomaterials. Their extraordinary behavior of lateral expansion in response to axial tension could potentially improve implant-bone contact in certain orthopedic applications. In this work, a multitude of auxetic meta-biomaterials were rationally designed and printed from Ti–6Al–4V using a commercially available laser powder bed fusion process called selective laser melting. The re-entrant hexagonal honeycomb unit cell was used as a starting point, which was then parametrically tuned to obtain a variety of mechanical and morphological properties. In this two-step study, the morphology and quasi-static properties of the developed meta-biomaterials were assessed using mechanical experiments accompanied with full-field strain measurements using digital image correlation. In addition, all our designs were computationally modelled using the finite element method. Our results showed the limits of the AM processes for the production of auxetic meta-biomaterials in terms of which values of the design parameters (e.g., re-entrant angle, relative density, and aspect ratio) could be successfully manufactured. We also found that the AM process itself imparts significant influence on the morphological and mechanical properties of the resulting auxetic meta-biomaterials. This further highlights the importance of experimental studies to determine the actual mechanical properties of such metamaterials. The elastic modulus and strength of many of our designs fell within the range of those reported for both trabecular and cortical bone. Unprecedented properties like these could be used to simultaneously address the different challenges faced in the mechanical design of orthopedic implants.Biomaterials & Tissue Biomechanic