# Failure Length and Primary Stability: An In Vitro Study on Polyurethane Foam
## 1 Introduction  
The achievement of primary stability during the dental-implant insertion is the first step toward a successful osseointegration [1]. Indeed, during the healing process, the absence of micromovements higher than 150 um is fundamental to achieve the formation of new bone [2]; on the contrary, a fibrous tissue of separation is produced, affecting the implant stability [3]. Moreover, a good glycemic control is fundamental to reduce implant failures in the first stages of healing [4]. Evidence supports the adoption of the second-stage protocol, with submersed implants during the healing stage, if primary stability is low [5]. Other authors suggest to solidarize the implants by means of metallic bars or intraoral electric welders in order to proceed directly to an immediate loading protocol (ILP) [5, 6]. The adoption of ILP of dental implantsneeds the presence of primary stability [7]. In particular, the literature suggests that, for ILP of full-arch restorations, the achievement of an insertion torque value (ITV) > 30 Ncm is necessary in order to avoid early failures [8; 9]. However, with the advent of novel implant surfaces, this value can further be reduced. The primary stability can be quantified with instruments that measure the frequency of resonance (RFA), such as the Ostell, or by measuring the \(\Pi\)TV and the removal torque value (RTV) [10; 11]. The primary stability is a direct consequence of the bone density and quality, implant design, and some specific surgical protocols, such as the under-preparation of the implant site, or the use of specific tools for bone osseedonsification, could be adopted in order to modify this parameter [1; 12]. In particular, the alveolar bone is characterized by an anisotropic behavior, and its mechanical features vary with the site of sampling and the testing orientation [13]; [PERSON] et al. showed, in 1999, that the modulus of elasticity of the bone ranged from 24.9 to 240.0 MPa with cortical plates present, and from 3.5 to 125.6 MPa without cortical plates [14]. However, the use of bone samples for in vitro studies that investigated the factors that influence the primary stability of dental implants has been considered as a possible bias, because of the impossibility to find natural samples with identical mechanical behavior, and also for ethical reasons [15]. In the last few years, the use of an artificial bone substitute, the polyurethane foam, characterized by a very similar mechanical behavior to natural bone, it has been proposed and validated for research in dental implantology [15; 16]. The parameters related to the fixture that influence the primary stability are the length, the presence of surface treatments, the shape of the implant, and other factors that could increase the surface area in contact with the bone [17; 18; 19]. In particular, recently, the use of fixtures with new superficial treatments that could accelerate the healing phase and/or decrease the bacterial interaction can permit us to achieve clinical success, also by starting by lower values of ITV [20; 21; 22]. Is has been shown that the process of double-etching treatment on titanium surfaces (DAE) is able to confer to the samples a multiscale roughness: that is the presence of a concomitant nano- and micro-topografy [20]. Moreover, novel post-processing techniques of the titanium implant permit production fixtures with a surface treatment that is locally differentiated. Traditionally, the stability of dental implants is considered to be directly correlated with the length; however, the insertion of long implants requires the presence of a greater quantity of bone, and if not present, the patient must undergo difficult bone-augmentation procedures, or more invasive interventions, such as the insertion of pterygoid or zygomatic fixtures [23; 24]. However, the insertion of long implants increases the risk of invasion of fragile structures, such as the mandibular canal, the mental foramen, and the maxillary sinus [25; 26].