## 1 Introduction  
In completely edentulous patients with a reduced alveolar ridge width, the insertion of four mini-dental implants (MDI) for mandibular overdenture (OD) retention and support is the alternative option to the insertion of two standard-sized implants [1; 2; 3; 4; 5; 6; 7; 8; 9; 10; 11]. Bone augmentation can be avoided by the insertion of narrow implants, which shortens the duration of treatment, providing a less traumatic surgical protocol [1; 2; 3; 4; 5]. Narrow dental implants (NDIs) are divided into three categories depending on their diameters: Category 3 (>3.3 mm-3.5 mm wide), Category 2 (>2.5 mm-<3.3 mm), and Category 1 (\(\leq\)2.5 mm wide) [12]. The one-piece mini-implants are listed in category 1, i.e., the narrowest NDI category (diameter \(\leq\) 2.5 mm) [12]. Narrow implants are usually made of Ti90 Al6V4 alloy, which has better mechanical properties than pure titanium. The insertion of four MDIs made of Ti90 Al6V4 alloy in the mandible has been approved as a successful treatment option for the retention of a mandibular OD in many prospective clinical studies [1; 2; 3; 4; 5; 6; 7; 8; 9; 10; 13; 14; 15]. Even the insertion of only three MDIs in the mandible for complete OD retention showed very good outcomes in a five-year clinical study [15]. Insertion of two MDIs showed good survival rates and low amounts of marginal bone loss only when used for retention of removable partial dentures [16; 17; 18]. However, the clinical outcomes of only two MDIs retaining a complete mandibular OD are still doubtful [19; 20; 21; 22]. To the best of our knowledge, no longitudinal clinical reports are available when only one MDI, inserted in the midline of the mandible, was used for the retention of a complete OD. In 2009, the Ti85 Zr15 alloy (Roxolid(r)) was introduced by the company Straumann Group. It showed very good mechanical properties and excellent osseointegration. Moreover, in many clinical prospective studies, narrow-diameter implants in categories 3 and 2 had very good performance when they supported fixed partial dentures [23; 24; 25]. Recently, in 2019, the new mini-implant system (category 1 of narrow implants, 2.4 mm wide) made of the Roxolid(r) (Ti-Zr) alloy (Straumann(r) Mini Implant System) was released on the dental market. Innovation of the new Ti-Zr MDIs included the new retention system (Straumann(r) Optiloc(r) Retentive System, i.e., prosthetic connection coated with an amorphous diamond-like carbon surface (ADLC) and a female PEEK matrix insert incorporated into titanium housing. The new mini-implant Ti-Zr system allows a choice of appropriate transmucosal heights. Four Roxolid(r) MDIs have been proposed for the retention of a mandibular OD, and six for the retention of a maxillary OD. Outcomes of four Roxolid(r) alloy MDIs retaining a mandibular OD in a prospective clinical study are available only for one year of their clinical use but with excellent results [26]. Due to the very good mechanical properties of the new Ti-Zr mini-implant system and the excellent osseointegration of the alloy, it would be interesting to find out whether less than the recommended four Ti-Zr mini-implants inserted in the mandible as single-units can successfully support a mandibular OD. In vitro studies are required before the safe clinical utilization of any new material, clinical technique or modification of any procedures [27; 28; 29]. Due to the difference in the stiffness of the implant material and the bone, the highest stress is distributed at the implant-bone interface. Peri-implant strains below 3000 microstrains represent the criterion for the long-term survival of any implant supporting a denture [27]. A model mimicking the \"in vivo\" situation and measuring peri-implant strains is beneficial to providing insights into the real clinical situation. Therefore, this \"in vitro\" study was designed to analyze microstrains around Ti-Zr mini-implants as well as microstrains in the posterior endulous area when different numbers of single-unit MDIs were inserted.