**1. Introduction**

Surgical treatments of bone injuries patients in emergency departments worldwide each year due to involvement in rigorous athletic activities, social instability, traffic accidents, and prolonged human lifespan [1].

Bone defects, mainly induced by traumatic avulsions, sequelae of infectioninduced bone sequestration, congenital malformations, or neoplastic resections, confront us with an extreme challenge for reconstructive surgery the need to induce bone regeneration to repair structural bone deficient [2] has inspired research on and development of a vast number of bone repair materials.

Diverse metallic materials are already established as biomaterials due to their high biocompatibility, low toxicity, and good strength–ductility relationship. Examples of these alloys are stainless steel (especially 316 L), cobalt and chromium (CoCr) alloys, and titanium (Ti) alloys [3, 4]. However, the low toxicity and mechanical properties of Ti alloys, specifically the elastic modulus, are more adequate for biomedical uses.

From Ti alloys, the most common for dental and orthopedic applications are materials formed by Ti, aluminum (Al) and vanadium (V) like Ti-6Al-4 V and other β-phasetype alloys as the ones with high contents of β-stabilizers (V, Cr, molybdenum (Mo), Fe, niobium (Nb), and tantalum (Ta)) [5–12]. However, several reports point to the V in the Ti-6Al-4 V as toxic [13, 14], being a motivation for exploring further V-free options. Moreover, the β-phase type Ti alloys have a good combination of mechanical properties and biocompatibility. Besides, the β-Ti alloys have a lower elastic modulus compared to other Ti alloys [15]. Considering that the elastic modulus is a key factor for the success or failure of the implant, this is a remarkable characteristic of these alloys [1]. However, the reported elastic modulus for β-Ti alloys ranges from 69 to 110 GPa [15, 16], being still far from that of human bone (lower than 30 GPa) [17].

To overcome this drawback, several Ti alloys are being developed and most of them are showing promising results in the matter of mechanical properties. A number of these metallic systems are being obtained through powder metallurgy methods to obtain functional porous structures. It has been widely reported that the porous surfaces assist on the fixations and ingrowth of organic tissue, improve the body fluid, reduce the mechanical mismatch due to lower elastic modulus values, and reduce the failure rate of implants [3]. Examples of the above are Ti and indium (In) as (Ti-In) [18], Ti-Mo [7–9], Ti, Nb and Tin (Sn) as Ti-Nb-Sn [10, 19], Ti and zirconium (Zr) as Ti-Zr [20], and Ti and silver (Ag) as Ti-Ag [21] alloys. However, some of the previous systems employ alloying elements that are still not widely studied, being a reason why several *in vivo* tests of biocompatibility should be carried out to determine their biological feasibility.

Another route is the design and development of biomaterials based on widely explore elements as magnesium (Mg). This element has multiple advantages for biomaterials as non-toxicity, biocompatibility, biodegradability, increase strength of the bone, and has a low elastic modulus [3, 4, 22–24]. Low concentrations of Mg2+ play an important role in cells activity by stimulating the improvement of cell adhesion and extracellular matrix mineralization [25, 26]. Furthermore, Mg is the fourth most abundant element in the human body and is essential in digestion processes [22, 24]. The non-harmful degradation of an Mg, zinc (Zn) and manganese (Mn) as Mg2Zn0.2Mn alloy inside the human body has been demonstrated [23]. Based on the above, Mg is a feasible alloying element to boost the biocompatibility and possible control of biodegradability over the time of different biomaterials for medical purposes. The biodegradability of Mg can avoid the need for a second surgical process to remove the implant. The possibility to control such biodegradability is still under intense investigation [23, 27, 28]. Moreover, Mg is a potential alloying element to significantly reduce the elastic modulus. This could reduce the failure rate due to mechanical mismatch between the implant and the bone, and the occurrence of load shielding (absorption of mechanical stress by the implant) [3]. However, one of the main disadvantages of Mg as a biomaterial is that the degradation rate can be faster than the required to allow a complete regeneration of the organic tissue [29]. This is the motivation to explore the use of Mg as an alloying element instead of a matrix. Considering the already explained qualities of Ti biomaterials, it is a good candidate to join with the virtues of Mg.

Until now, few reports on Mg as an alloying element of Ti alloys have been reported [30–33]. Deep research is still needed in the matter of optimizing Mg contents, processing parameters, and designing new systems that reduce the economic and health losses due to the failure of implants. The field of Ti-Mg alloys is emerging and is pointing as highly promising for biomedical purposes.
