**1. Introduction**

The increasingly elderly population and the accompanying rising number of bone fractures have led to a significant rise in physical disabilities. The healing of larger bone defects is still a challenging task in orthopaedics. Using degradable implants eliminates the need for revision surgery, which may be required for some permanent medical devices. Thus, using such implants would not only benefit the patient, but also reduce healthcare costs [1]. Ideally, the implants should present a fully interconnected porous structure and should show equivalent mechanical properties, especially regarding the stiffness [2]. Such a biodegradable bone implant would allow fully natural bone regeneration, while the material gradually disappears in the body through absorption. These requirements can be fulfilled i.e., by additive manufactured (AM) lattice structures. Due to the large number of available materials and design parameters, almost any mechanical and material requirement profile can be set. However, biocompatibility and an interconnected porous structure can be fulfilled by a wide range of materials, reaching equivalent mechanical

**Citation:** Bühring, J.; Voshage, M.; Schleifenbaum, J.H.; Jahr, H.; Schröder, K.-U. Influence of Degradation Product Thickness on the Elastic Stiffness of Porous Absorbable Scaffolds Made from an Bioabsorbable Zn–Mg Alloy. *Materials* **2021**, *14*, 6027. https://doi.org/ 10.3390/ma14206027

Academic Editor: Marián Palcut

Received: 19 August 2021 Accepted: 8 October 2021 Published: 13 October 2021

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properties at the same time is still challenging. Biocompatible materials can be found in a wide variety of material classes [3]. One example are polymer-based materials, which offer great advantages in terms of customized biodegradation and design [4]. Further to mention are ceramic materials, which also exhibit the aforementioned biodegradation and offer particularly good healing properties for bone defects [5]. However, for fully load-bearing applications only metals fulfill the needed properties, especially regarding strength and stiffness [6]. The Laser Powder Bed Fusion (LPBF) process enables the individualized production of high-resolution lattice structures with very fine struts (<250 μm) [7,8] at reasonable costs, and is thus ideal for the production of personalized implants [9]. In particular, the use of zinc (Zn), magnesium (Mg), iron (Fe) and their alloys, are increasingly coming into focus for orthopaedic applications [10,11]. Although Fe-based implants would biomechanically, and with respect to their corrosion speed [12,13], gain most from increased porosity [14], their limited cytocompatibility is a concern [15]. Nevertheless, in comparison to pure zinc and magnesium, iron has the highest values regarding yield strength and Young's modulus (*σy*,*Fe* ≈ 200–352 MPa, *EFe* ≈ 188–215 GPa [16–18]; *σy*,*Zn* ≈ 12–32 MPa, *EZn* ≈ 43–150 GPa [12,18,19]; *σy*,*Mg* ≈ 51 MPa, *EMg* ≈ 27–35 GPa [20–22]) and offers a large margin for introducing a controlled porosity, which directly influences the strength and stiffness properties of the material. Alloying can further improve the mechanical properties. Adding Zn to Mg-based alloys increases the yield strength and Young's modulus of the material [3,13,23]. Same goes for Zn alloyed with Mg [3,19,24], whereas adding aluminum to Zn-based alloys leads to a decrease in stiffness and strength [19].

Examples for Mg- and Zn-based studies on porous scaffolds can be found, e.g., in Witte et al. [25], who show the feasibility of producing AM open-porous, biodegradable and biocompatible Mg scaffolds. Li et al. [2] produced AM WE43 (Mg alloy with 4 wt% yttrium and 3 wt% rare earth elements) scaffolds based on diamond unit cells, to show the in vitro biodegradation behavior, mechanical properties and biocompatibility. Furthermore, Kopp et al. [26] showed that the pore size of Mg scaffolds influences the long-term stability, while heat treatment especially effects the degradation and mechanical stability. Cockerill et al. [27] used a casting approach to produce porous structures made of pure Zn and studied the topology, mechanical properties, biodegradation and biocompatibility. Another example is shown by Li et al. [28], who produced scaffolds from Zn with a diamond lattice structure via LPBF and studied the static and dynamic biodegradation behavior.

In a physiological environment biodegradable metals usually show a decreasing Young's modulus during the degradation process, due to the progressive absorption of the metallic surface, which consequently leads to a reduction of the strut cross section [29–32]. Since the strut thickness is directly related to the stiffness, the latter will also decrease. Interestingly, during the first days of in vitro corrosion of Mg-based (WE43) scaffolds, an increase of around 40% in the Young's modulus was recently reported [2]. This increase in stiffness is mainly attributed to the formation of a composite cross section, consisting of the base strut and an adherend layer of degradation products. A brief review of the literature shows [3,10,29,31] that the compound of degradation products, which adheres to the surface of the struts, consists for the most parts of hydroxides, phosphates and carbonates, for which only insufficient mechanical properties can be found. The phosphates and carbonates form a compound of usually unspecified chemical composition that further changes over time. Furthermore, a hydroxide layer is forming on the metallic surface. The basic biochemical processes, responsible for this, can be summarized as followed [29,31,32]:


Figure 1 shows a simplified schematic of the degradation process. The human body fluid releases an anodic reaction, and the free electrons undergo a cathodic reaction under the release of hydrogen and hydroxide ions, which form together with the metal a hydroxide layer on the surfaces of the struts. From equivalent reactions, phosphates and carbonates form on the strut surfaces [29]. These processes are responsible for an increase in stiffness during the early phases of the corrosion process [2]. Later, chloride ions start the dissolution of the biodegradable metal to cause a decrease of the cross-sectional strut diameter of the scaffold.

**Figure 1.** Schematic process sketch of the degradation process of absorbable metals according to Han et al. and Li [29,31].

We now used Zn1Mg (1 wt% Mg) as an example to investigate the influence of degradation products on the elastic stiffness properties of metallic scaffolds using analytical calculations and finite-element (FE) simulations. For this, first, we focused on the direct influence of the forming substrate layer of degradation products on the axial and bending stiffness of single struts. The corroded strut is modeled as a composite beam with a solid Zn1Mg base strut and a thin-walled layer of corrosion products of unspecified chemical composition. Instead of using concretely quantified values for the Young's modulus for the compound of degradation products, hypothetical multiples of the Zn1Mg Young's modulus are used. Afterwards, a new scaffold geometry, based on a polar modeling of a f2cc,z unit cell is produced and tested, to validate the FE model. Using the validated model, a FE parametric study is done to investigate the influence of the substrate layer thickness and Young's modulus of the compound on the smeared Young's modulus of the scaffold.
