Behdad Pouran

Relationship between unit cell type and porosity and the fatigue behavior of selective laser melted meta-biomaterials

Meta-materials are structures when their small-scale properties are considered, but behave as materials when their homogenized macroscopic properties are studied. There is an intimate relationship between the design of the small-scale structure and the homogenized properties of such materials. In this article, we studied that relationship for meta-biomaterials that are aimed for biomedical applications, otherwise known as meta-biomaterials. Selective laser melted porous titanium (Ti6Al4V ELI) structures were manufactured based on three different types of repeating unit cells, namely cube, diamond, and truncated cuboctahedron, and with different porosities. The morphological features, static mechanical properties, and fatigue behavior of the porous biomaterials were studied with a focus on their fatigue behavior. It was observed that, in addition to static mechanical properties, the fatigue properties of the porous biomaterials are highly dependent on the type of unit cell as well as on porosity. None of the porous structures based on the cube unit cell failed after 10(6) loading cycles even when the applied stress reached 80% of their yield strengths. For both other unit cells, higher porosities resulted in shorter fatigue lives for the same level of applied stress. When normalized with respect to their yield stresses, the S-N data points of structures with different porosities very well (R(2)>0.8) conformed to one single power law specific to the type of the unit cell. For the same level of normalized applied stress, the truncated cuboctahedron unit cell resulted in a longer fatigue life as compared to the diamond unit cell. In a similar comparison, the fatigue lives of the porous structures based on both truncated cuboctahedron and diamond unit cells were longer than that of the porous structures based on the rhombic dodecahedron unit cell (determined in a previous study). The data presented in this study could serve as a basis for design of porous biomaterials as well as for corroboration of relevant analytical and computational models.

Additively Manufactured Open-Cell Porous Biomaterials Made from Six Different Space-Filling Unit Cells: The Mechanical and Morphological Properties

It is known that the mechanical properties of bone-mimicking porous biomaterials are a function of the morphological properties of the porous structure, including the configuration and size of the repeating unit cell from which they are made. However, the literature on this topic is limited, primarily because of the challenge in fabricating porous biomaterials with arbitrarily complex morphological designs. In the present work, we studied the relationship between relative density (RD) of porous Ti6Al4V EFI alloy and five compressive properties of the material, namely elastic gradient or modulus (Es20–70), first maximum stress, plateau stress, yield stress, and energy absorption. Porous structures with different RD and six different unit cell configurations (cubic (C), diamond (D), truncated cube (TC), truncated cuboctahedron (TCO), rhombic dodecahedron (RD), and rhombicuboctahedron (RCO)) were fabricated using selective laser melting. Each of the compressive properties increased with increase in RD, the relationship being of a power law type. Clear trends were seen in the influence of unit cell configuration and porosity on each of the compressive properties. For example, in terms of Es20–70, the structures may be divided into two groups: those that are stiff (comprising those made using C, TC, TCO, and RCO unit cell) and those that are compliant (comprising those made using D and RD unit cell).

Endochondral bone formation in gelatin methacrylamide hydrogel with embedded cartilage-derived matrix particles

The natural process of endochondral bone formation in the growing skeletal system is increasingly inspiring the field of bone tissue engineering. However, in order to create relevant-size bone grafts, a cell carrier is required that ensures a high diffusion rate and facilitates matrix formation, balanced by its degradation. Therefore, we set out to engineer endochondral bone in gelatin methacrylamide (GelMA) hydrogels with embedded multipotent stromal cells (MSCs) and cartilage-derived matrix (CDM) particles. CDM particles were found to stimulate the formation of a cartilage template by MSCs in the GelMA hydrogel in vitro. In a subcutaneous rat model, this template was subsequently remodeled into mineralized bone tissue, including bone-marrow cavities. The GelMA was almost fully degraded during this process. There was no significant difference in the degree of calcification in GelMA with or without CDM particles: 42.5 ± 2.5% vs. 39.5 ± 8.3% (mean ± standard deviation), respectively. Interestingly, in an osteochondral setting, the presence of chondrocytes in one half of the constructs fully impeded bone formation in the other half by MSCs. This work offers a new avenue for the engineering of relevant-size bone grafts, by the formation of endochondral bone within a degradable hydrogel.

Additively manufactured metallic porous biomaterials based on minimal surfaces : A unique combination of topological, mechanical, and mass transport properties

Porous biomaterials that simultaneously mimic the topological, mechanical, and mass transport properties of bone are in great demand but are rarely found in the literature. In this study, we rationally designed and additively manufactured (AM) porous metallic biomaterials based on four different types of triply periodic minimal surfaces (TPMS) that mimic the properties of bone to an unprecedented level of multi-physics detail. Sixteen different types of porous biomaterials were rationally designed and fabricated using selective laser melting (SLM) from a titanium alloy (Ti-6Al-4V). The topology, quasi-static mechanical properties, fatigue resistance, and permeability of the developed biomaterials were then characterized. In terms of topology, the biomaterials resembled the morphological properties of trabecular bone including mean surface curvatures close to zero. The biomaterials showed a favorable but rare combination of relatively low elastic properties in the range of those observed for trabecular bone and high yield strengths exceeding those reported for cortical bone. This combination allows for simultaneously avoiding stress shielding, while providing ample mechanical support for bone tissue regeneration and osseointegration. Furthermore, as opposed to other AM porous biomaterials developed to date for which the fatigue endurance limit has been found to be ≈20% of their yield (or plateau) stress, some of the biomaterials developed in the current study show extremely high fatigue resistance with endurance limits up to 60% of their yield stress. It was also found that the permeability values measured for the developed biomaterials were in the range of values reported for trabecular bone. In summary, the developed porous metallic biomaterials based on TPMS mimic the topological, mechanical, and physical properties of trabecular bone to a great degree. These properties make them potential candidates to be applied as parts of orthopedic implants and/or as bone-substituting biomaterials. STATEMENT OF SIGNIFICANCE Bone-substituting biomaterials aim to mimic bone properties. Although mimicking some of bone properties is feasible, biomaterials that could simultaneously mimic all or most of the relevant bone properties are rare. We used rational design and additive manufacturing to develop porous metallic biomaterials that exhibit an interesting combination of topological, mechanical, and mass transport properties. The topology of the developed biomaterials resembles that of trabecular bone including a mean curvature close to zero. Moreover, the developed biomaterials show an unusual combination of low elastic modulus to avoid stress shielding and high strength to provide mechanical support. The fatigue resistance of the developed biomaterials is also exceptionally high, while their permeability is in the range of values reported for bone.

Fatigue performance of additively manufactured meta-biomaterials: The effects of topology and material type

Additive manufacturing (AM) techniques enable fabrication of bone-mimicking meta-biomaterials with unprecedented combinations of topological, mechanical, and mass transport properties. The mechanical performance of AM meta-biomaterials is a direct function of their topological design. It is, however, not clear to what extent the material type is important in determining the fatigue behavior of such biomaterials. We therefore aimed to determine the isolated and modulated effects of topological design and material type on the fatigue response of metallic meta-biomaterials fabricated with selective laser melting. Towards that end, we designed and additively manufactured Co-Cr meta-biomaterials with three types of repeating unit cells and three to four porosities per type of repeating unit cell. The AM meta-biomaterials were then mechanically tested to obtain their normalized S-N curves. The obtained S-N curves of Co-Cr meta-biomaterials were compared to those of meta-biomaterials with same topological designs but made from other materials, i.e. Ti-6Al-4V, tantalum, and pure titanium, available from our previous studies. We found the material type to be far more important than the topological design in determining the normalized fatigue strength of our AM metallic meta-biomaterials. This is the opposite of what we have found for the quasi-static mechanical properties of the same meta-biomaterials. The effects of material type, manufacturing imperfections, and topological design were different in the high and low cycle fatigue regions. That is likely because the cyclic response of meta-biomaterials depends not only on the static and fatigue strengths of the bulk material but also on other factors that may include strut roughness, distribution of the micro-pores created inside the struts during the AM process, and plasticity. STATEMENT OF SIGNIFICANCE Meta-biomaterials are a special class of metamaterials with unusual or unprecedented combinations of mechanical, physical (e.g. mass transport), and biological properties. Topologically complex and additively manufactured meta-biomaterials have been shown to improve bone regeneration and osseointegration. The mechanical properties of such biomaterials are directly related to their topological design and material type. However, previous studies of such biomaterials have largely neglected the effects of material type, instead focusing on topological design. We show here that neglecting the effects of material type is unjustified. We studied the isolated and combined effects of topological design and material type on the normalized S-N curves of metallic bone-mimicking biomaterials and found them to be more strongly dependent on the material type than topological design.

Transport of Neutral Solute Across Articular Cartilage: The Role of Zonal Diffusivities

Transport of solutes through diffusion is an important metabolic mechanism for the avascular cartilage tissue. Three types of interconnected physical phenomena, namely mechanical, electrical, and chemical, are all involved in the physics of transport in cartilage. In this study, we use a carefully designed experimental-computational setup to separate the effects of mechanical and chemical factors from those of electrical charges. Axial diffusion of a neutral solute Iodixanol into cartilage was monitored using calibrated microcomputed tomography micro-CT images for up to 48 hr. A biphasic-solute computational model was fitted to the experimental data to determine the diffusion coefficients of cartilage. Cartilage was modeled either using one single diffusion coefficient (single-zone model) or using three diffusion coefficients corresponding to superficial, middle, and deep cartilage zones (multizone model). It was observed that the single-zone model cannot capture the entire concentration-time curve and under-predicts the near-equilibrium concentration values, whereas the multizone model could very well match the experimental data. The diffusion coefficient of the superficial zone was found to be at least one order of magnitude larger than that of the middle zone. Since neutral solutes were used, glycosaminoglycan (GAG) content cannot be the primary reason behind such large differences between the diffusion coefficients of the different cartilage zones. It is therefore concluded that other features of the different cartilage zones such as water content and the organization (orientation) of collagen fibers may be enough to cause large differences in diffusion coefficients through the cartilage thickness.

Isolated effects of external bath osmolality, solute concentration, and electrical charge on solute transport across articular cartilage

The metabolic function of cartilage primarily depends on transport of solutes through diffusion mechanism. In the current study, we use contrast enhanced micro-computed tomography to determine equilibrium concentration of solutes through different cartilage zones and solute flux in the cartilage, using osteochondral plugs from equine femoral condyles. Diffusion experiments were performed with two solutes of different charge and approximately equal molecular weight, namely iodixanol (neutral) and ioxaglate (charge=-1) in order to isolate the effects of solutes charge on diffusion. Furthermore, solute concentrations as well as bath osmolality were changed to isolate the effects of steric hindrance on diffusion. Bath concentration and bath osmolality only had minor effects on the diffusion of the neutral solute through cartilage at the surface, middle and deep zones, indicating that the diffusion of the neutral solute was mainly Fickian. The negatively charged solute diffused considerably slower through cartilage than the neutral solute, indicating a large non-Fickian contribution in the diffusion of charged molecules. The numerical models determined maximum solute flux in the superficial zone up to a factor of 2.5 lower for the negatively charged solutes (charge=-1) as compared to the neutral solutes confirming the importance of charge-matrix interaction in diffusion of molecules across cartilage.

Effects of applied stress ratio on the fatigue behavior of additively manufactured porous biomaterials under compressive loading

Additively manufactured (AM) porous metallic biomaterials are considered promising candidates for bone substitution. In particular, AM porous titanium can be designed to exhibit mechanical properties similar to bone. There is some experimental data available in the literature regarding the fatigue behavior of AM porous titanium, but the effect of stress ratio on the fatigue behavior of those materials has not been studied before. In this paper, we study the effect of applied stress ratio on the compression-compression fatigue behavior of selective laser melted porous titanium (Ti-6Al-4V) based on the diamond unit cell. The porous titanium biomaterial is treated as a meta-material in the context of this work, meaning that R-ratios are calculated based on the applied stresses acting on a homogenized volume. After morphological characterization using micro computed tomography and quasi-static mechanical testing, the porous structures were tested under cyclic loading using five different stress ratios, i.e. R = 0.1, 0.3, 0.5, 0.7 and 0.8, to determine their S-N curves. Feature tracking algorithms were used for full-field deformation measurements during the fatigue tests. It was observed that the S-N curves of the porous structures shift upwards as the stress ratio increases. The stress amplitude was the most important factor determining the fatigue life. Constant fatigue life diagrams were constructed and compared with similar diagrams for bulk Ti-6Al-4V. Contrary to the bulk material, there was limited dependency of the constant life diagrams to mean stress. The notches present in the AM biomaterials were the sites of crack initiation. This observation and other evidence suggest that the notches created by the AM process cause the insensitivity of the fatigue life diagrams to mean stress. Feature tracking algorithms visualized the deformation during fatigue tests and demonstrated the root cause of inclined (45°) planes of specimen failure. In conclusion, the R-ratio behavior of AM porous biomaterials is both quantitatively and qualitatively different from that of bulk materials.

Guidelines for an optimized indentation protocol for measurement of cartilage stiffness: The effects of spatial variation and indentation parameters

Mechanical properties of articular cartilage that are vital to its function are often determined by indentation tests, which can be performed at different scales. Cartilage tissue exhibits various types of structural, geometrical, and spatial variations that pose strict demands on indentation protocols. This study aims to define a reproducible micro-indentation protocol for measuring the effective (average) stiffness of the cartilage surface in a region around 1mm2. We elucidated how different parameters such as indenter size, indenter depth, and the location of the indentation influence the effective elastic modulus measured in micrometer scale on rat knee cartilage. When an indentation was performed (50μm radial probe, ≈10μm indentation depth) at exactly the same location, the variability was less than 10%, even with a recovery period of 30s. However, there was a high spatial variation and a small change of around 60μm in location could change the modulus values up to as much as 10-20 fold. The effective elastic modulus of cartilage surface layer cannot therefore be reproducibly determined from a few indentations on a cartilage sample, and requires at least 144 (12×12) indentations for a soft spherical probe with a 50μm radius. With higher depths, the spatial variation is slightly lower, allowing slightly lower number of indentations (≈80 measurements or a 9×9 frame) to provide a representative elastic modulus. Using this protocol, we determined an elastic modulus of 2.6±1.9N/mm2 at the medial side versus a higher modulus of 4.2±2.6N/mm2 at the lateral side of the tibia of 12 weeks old Wistar rats. Optimized indentation protocols similar to the one presented here are required for revealing such variations in the mechanical properties of cartilage with anatomical location.

Isolated and modulated effects of topology and material type on the mechanical properties of additively manufactured porous biomaterials

In this study, we tried to quantify the isolated and modulated effects of topological design and material type on the mechanical properties of AM porous biomaterials. Towards this aim, we assembled a large dataset comprising the mechanical properties of AM porous biomaterials with different topological designs (i.e. different unit cell types and relative densities) and material types. Porous structures were additively manufactured from Co-Cr using a selective laser melting (SLM) machine and tested under quasi-static compression. The normalized mechanical properties obtained from those structures were compared with mechanical properties available from our previous studies for porous structures made from Ti-6Al-4V and pure titanium as well as with analytical solutions. The normalized values of elastic modulus and yield stress were found to be relatively close to each other as well as in agreement with analytical solutions regardless of material type. However, the material type was found to systematically affect the mechanical properties of AM porous biomaterials in general and the post-elastic/post-yield range (plateau stress and energy absorption capacity) in particular. To put this in perspective, topological design could cause up to 10-fold difference in the mechanical properties of AM porous biomaterials while up to 2-fold difference was observed as a consequence of changing the material type.