## 2 Design Method of Pilot Oxygen Mask Based on Virtual Fit Analysis
### Ergonomic Mask Design by Virtual Fit Analysis  
A virtual fit analysis method is developed to find the most ergonomically optimized boundary of the mask by virtually fitting the mask to various 3D faces. First, the boundary of a mask is virtually located over a 3D face at the identified mask-wearing positions. After virtual fitting of the mask to the face, the horizontal distances between the boundary of the mask and the surface of the 3D face are calculated along the vertical axis with an interval of 1% of the mask length, as illustrated in Figure 3a; in the plot, the facial area of which horizontal distance <0 mm (red area in Figure 3a) indicates the mask boundary region not contacting the face (causing oxygen leakage), while the opposite penetrating the face (causing contact pressure to the face). Next, the interface area of the mask and the face is divided into five sections along with the vertical location from the top: 0% to 10% for the nasal root area, 10% to 50% for the nasal side area, 50% to 90% for the cheek area, and 90% to 100% for the chin area. Figure 3b plots the horizontal distances of a designated group of faces (e.g., \(n=29\) pilot faces belonging to the small narrow size group) from the mask boundary, showing negative horizontal distances at the nasal root and positive horizontal distances at the other face sections. A virtual fit analysis program was coded using MATLAB (MathWorks, Inc., Natick, MA, USA) in the present study to analyze horizontal distances between the mask boundary and 3D face surfaces.  
An ergonomically optimized shape of the mask boundary for a designated user group is searched by an iterative design process and virtual fit analysis shown in Figure 4. In the first step (S1), an initial shape of the mask boundary is prepared by generating a spline curve that connects the design landmarks corresponding with positions on the face with the average size for the user group. In the second step (S2), the horizontal distances between the mask boundary and 3D face surfaces of the user group are calculated. In the third step  
Figure 2: Identification of mask-wearing positions using 3D scan images of a pilot face and an oxygen mask (illustrated). (**a**) 3D scan image of an oxygen mask; (**b**) 3D face scan image without wearing the mask; (**c**) 3D face scan image wearing the oxygen mask; (**d**) 3D scan images of the mask and the face overlaid to the 3D face scan image wearing the mask; (**e**) identification of the mask-wearing positions based on the mask design landmarks (**) and facial landmarks (\(l\)).  
(S3), the plots of the horizontal distances are evaluated to determine the appropriateness of the mask boundary for the designated user group. Note that the present study used a range of proper fit along the face sections identified by a usability evaluation survey of the MBU-20/P oxygen mask (described in Section 3.2) to evaluate the appropriateness of a mask boundary. In the fourth step (S4), the mask boundary is modified by adjusting the locations of the design landmarks in case that the mask boundary is found unsatisfactory for the designated user group. Repeat S2 to S4 until a satisfactory mask boundary is found. Lastly, in the fifth step (S5), a complete design of the mask is developed based on the selected mask boundary.  
Figure 4: An ergonomic design process of a pilot oxygen mask by virtual fit analysis.  
Figure 3: Virtual fit analysis by calculating horizontal distances between the mask boundary and 3D face surfaces (illustrated). (**a**) Horizontal distances between the mask boundary and the face surface along the vertical axis with an interval of 1% of the mask length (blue line: mask boundary; red line: face surface, red shaded area: mask boundary region of negative horizontal distances causing oxygen leakage; blue shaded area: mask boundary region of positive horizontal distances causing contact pressure to the face); (**b**) plots of the horizontal distances between the mask boundary and face surfaces of a small narrow size group (\(n=29\)).