## 2 Materials and Methods
### Surgical Procedures  
Group A: Sinus floor elevation through a Lateral Window Technique  
All surgical procedures were performed by the same surgeon with advanced surgical experience. As for the other surgery types, one hour prior, patients received 2 g amoxicillin and clavulanic acid, and they received another 1 g twice a day for a week after the surgical procedure (clarithromycin was prescribed as an alternative in case of allergy, 2 g before surgery and 1 g twice a day for the following week). Surgery was performed under anesthesia induced by local infiltration of opticain solution with adrenaline 1:80,000 (AstraZeneca, Milan, Italy). The same protocol was applied for all techniques. The first incision was made on the top of the alveolar crest, shifted on the palatal side to obtain the same level of keratinized mucosa on both flap sides. Then, distal and mesial vertical release incisions were performed to expose the underlying bone crest. The full-thickness flap was elevated to preserve anatomical subperiosteal structures. The flap was detached to expose the anterior piriform cortex and canine draft, used as landmarks, and to identify the maxillary sinus, often available in transparency from the lateral bone wall. A bony window was drawn using a sterile pencil on the lateral wall, behind the canine draft, according to the size and location of the maxillary sinus and the implant insertion site. Then, a high-speed handpiece with a diamond bur was employed to outline the antrostomy. A bone scraper was used to obtain autologous bone chips from the bony window. To preserve the Schneiderian membrane from injuries, a piezoelectric instrument was employed for bony window detachment. The elevation degree was set according to the vertical defect's extension, proceeding from the inferior-medial sinus wall to the distal. The implant sites were prepared using a lance-shaped drill followed by drills of increasing diameter; fixtures were then placed. The implants placed for this group belonged to the K line (Winsix, Biosafin, Ancona, Italy); this implant type has a cylindrical shape with a truncated conical body characterized by a self-threading coil with differentiated depth and thickness and variable geometry to modulate primary stability during surgery. The macromorphology is characterized by variable geometry, the coils gradually varying from square to triangular and varying in depth to favor vertical micro-expansion and progressive horizontal expansion; it has wide and deep unloading grooves for the deposition of bone chips and the formation of clots during the screwing phase. Due to the properties of these implants, they were chosen for both methods of sinus lift (lateral approach and transcrastal approach), by agreement of the surgeon and prosthetic. The autologous bone graft obtained from the bony window was the only biomaterial applied, and it was placed around implants to promote bone regeneration [24]. An adsorbable hemostatic gelatin (Spongostan, Ethicon, Johnson & Johnson, New Brunswick, NJ, USA) was employed to promote clot formation and to contain the exposed sinus area following the removal of the bony opening that provided access to the cavity. Flap adaptation and suturing were performed using 3-0 non-resorbable sutures (Vicryl; Ethicon, Johnson & Johnson, New Brunswick, NJ, USA). Group B: Sinus floor elevation through an Osteotome-Mediated Technique  
The first incision was made on the top of the alveolar crest, shifted on the palatal side to obtain the same level of keratinized mucosa on both sides of the flap. Distal and mesial vertical release incisions were performed to create a full-thickness flap, exposing the underlying bone crest and preserving anatomical epiperiosteal structures. A lance-shaped drill was employed for 2 mm to drill the cortical bone. A pilot drill of a 2.00 was applied to create an implant insertion site and to define the fixture's setting. Then, osteotomes of progressively increasing diameter were gradually driven to sinus floor fracture and Schneiderian membrane elevation.