## 2 Design and Implementation
### System Implementation  
Figure 7 shows the iTDS-2 SoC, which has been implemented in a 0.35- \(\upmu\)m 2P3M std. CMOS process, with the chip area of 5.0 \(\times\)2.4 mm\({}^{2}\), including PADs. Figure 8 shows the iTDS-2 prototype, implemented as an arch-shaped dental retainer, to be mounted on the buccal shelf. The arch-shaped dental retainer is made of orthodontic Ortho-Jet crystal powder and liquid (Lang Dental, Wheeling, IL, USA) with two stainless still ball claps (Patterson Dental Supply, St. Paul, MN, USA). The Ortho-Jet crystal covers the iTDS-2 electronics and protects them from external forces and the saliva, while the two ball claps help fix the iTDS-2 onto the lower molar teeth. The iTDS-2 uses smaller ball claps than usual (\(\phi\) = 0.7 mm) because it utilizes inward clamping, while dental retainers such as Hawley retainer often utilize outward clamping. To determine the maximum allowable size of the PCB and electronics, we reviewed literature on the buccal shelf area, which is defined as the space bounded on the medial side by the crest of the residual ridge, on the lateral side by the external oblique ridge, in the mesial area by the buccal frenum, and on the distal side by the masseter muscle [31]. The length of the buccal shelf area is about the length of three consecutive molar teeth, reported as \(\sim\)30 mm, on average [52]. The height of the buccal shelf area  
Figure 6: _Cont._  
can be defined as the total height of molar teeth including both the crown and root lengths. According to [53], the heights of the 1 st, 2 nd, and 3 rd molars were 19.3 mm, 18.4 mm, and 17.2 mm, respectively, in 46 healthy individuals. We considered the data on the thickness of dentures to find information on the depth of the buccal shelf area, which are \(\sim\)3 mm over the 1 st and 2 nd molars and 6.3 mm over the 3 rd molar [54]. However, we understand that the data derived from dentures can differ from the data from people with normal teeth, because the shape of the buccal shelf gradually transforms in the absence of the teeth. Another important consideration, which was not included in this study, is the difference between the oral anatomy and available oral space in men and women. Moreover, although these numbers helped us in design of the iTDS-2 prototype, we still need to customize the iTDS-2 for each potential user because everyone has a different oral anatomy. Figure 8: iTDS-2 prototypes with custom PCBs, electronics, a rechargeable Li-Ion battery, and a PIFA antenna, all hermetically sealed in the form of an arch-shaped dental retainer. Figure 7: Die photo of the iTDS-2 system-on-a-chip, implemented in a 0.35- μm 2P3M std. The conclusion from this data for an average adult to wear the iTDS-2 with minimum discomfort was 28 mm \(\times\)14 mm \(\times\)2 mm in length, height, and thickness, respectively. Moreover, as shown in Figure 8, both control and supply boards on the right and left sides of the retainer, respectively, were tapered on the posterior side, as a trapezoids, considering the shape of the buccal shelf area [31]. The Ortho-Jet crystal layer over the electronics was made thin to minimize the retainer volume while it still provides the mechanical support. The arch-shaped bridge across two boards, which supports two 5.5 mm wide, 10-wire flat cable interconnects, was designed to be very close to the lower teeth to minimize protrusion towards the lower lips. The overall volume of the arch-shaped iTDS-2 dental retainer prototype was measured 12 mL, which is 40% smaller than the iTDS-1 palatal retainer (20 mL), reported in [12]. The control board, located on the right buccal shelf area, includes the iTDS-2 SoC, an IGLOO nano (Microsemi, Aliso Viejo, CA, USA) FPGA, three crystals, and two magnetometers. The supply board, located on the opposite side, includes a 50 mAh rechargeable Li-Ion battery (12 \(\times\)15 \(\times\)5 mm\({}^{3}\)) and two magnetometers.