The Coronavirus disease-2019 (COVID-19) has sickened over 6 million people around 2 the world, with several hundred thousand hospitalizations. The rapid influx of patients 3 to hospitals and intensive care units has resulted in a high demand for personal 4 protective equipment (PPE) with constant supply-chain pressure leading to shortages 5 and rationing. Fitted N95 masks which block aerosolized virus-containing droplets are 6 of particular importance in protecting clinicians and front-line workers from being 7 infected with and spreading this dangerous pathogen. While traditionally considered 8 single-use items, some research has looked at and tested the possibility of sanitizing 9 masks for re-use [1] [2] [3] [4] [5] . This is not yet a common practice as techniques are evolving and 10 the availability of necessary equipment is likely site specific. favor since it is rapid and effective for sterilizing hard surfaces, making it an ideal choice 14 for repeated sanitization of rooms [6] . Light at wavelengths within the UV-C band 15 inactivate viruses through DNA and RNA lysis. However, N95 masks and surgical 16 masks are engineered with complex geometries and with layers of porous material. This 17 creates layers within the thickness of the mask material where germs or viral particles 18 might penetrate and reside. If the UV-C light does not sufficiently penetrate the mask 19 material, the viral particles and infectious agents that can become embedded within the 20 layers of N95 masks may be untreated by traditional UV-C sterilization protocols 21 designed for treating hard surfaces.
Because UV-C light is highly absorbed by most material, this attenuation-an 23 exponential function of material thickness and type-and some degree of light scatter 24 must be considered in effective treatment planning for masks sterilization using UV-C 25 light. Adaptation of existing UV-C systems to this purpose [7, 8] , however, allows mask 26 sterilization to be done at the point of care, employing equipment already within many 27 hospitals around the world. Here we report simulations of treatment with a focus on the 28 sanitization of the entire mask, including interior layers. Our findings highlight several 29 issues with simple illumination configurations [1] while describing an efficient protocol 30 for operation of UV-C treatment of masks.
Setup 33 We used mathematical and computational modeling to predict the attenuation of UV-C 34 light rays in a decontamination apparatus where masks are suspended along parallel 35 lateral supports (Fig 1) with UV-C lamps placed on either side. We considered a 36 treatment array that is 200 cm wide x 100 cm high and targeted a minimum UV-C dose 37 of 20 mJ/cm 2 [9, 10] , up to 4x the decimation dose for viruses such as SARS-CoV-2, We used Tru-D UV-C robots (Tru-D SmartUVC, Memphis, TN), designed for room 40 irradiation and sterilization, to illuminate the masks, and calibrated the total intensity 41 of each lamp using a Gigahertz-Optik X11-1-UV3718 radiometer (Turkenfeld, Germany). 42 Lamps typically produced 2.7 J/cm 2 over 5 minutes of exposure at a distance of 55 cm 43 and an elevation of 90 cm, half the height of the lamp. Treatment dose is additive and 44 any number of lamps may be used, although we used one lamp on each side of the 45 treatment array while performing protocols with either single or multiple stations.
Masks may be more difficult to treat depending on their curvature and layered 47 composition. We chose to perform our simulations using the 3M model 1860 because we 48 found it more challenging to decontaminate than other N95 masks such as the Moldex 49 model 2200. The Moldex N95 mask has comparable curvature and thickness, but is 50 significantly more transparent to UV-C light than the 3M version, which improves 51 exposure of the mask interior. We selected Halyard tie-back masks as a representative 52 flat folded surgical mask.
We modeled the dose received by each part of a medical mask by considering the 55 emission of ultraviolet light from a UV-C lamp, the path it took to reach its mask 56 target, and the angle of incidence θ at the mask surface. Energy emitted from the UV-C 57 lamps is assumed approximately uniform over all angles from each section of its mercury 58 vapor bulbs. Lamps are composed of 14 tubes, each of which was discretized into 20 59 light sources. Therefore each mask segment receives 14x20 light rays of distinct 60 October 30, 2020 2/8 . CC-BY-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.
The copyright holder for this preprint this version posted November 4, 2020. a) The apparatus setup, showing a treatment array and two lamps marked by (*) b) a curved mask exposed to one UV-C lamp on each side. Due to the mask curvature, some areas are not directly exposed to the light rays of the two lamps. c) UV-C light ray (orange arrow) is refracted and penetrates the mask panel fabric.
Attenuation of light at a given depth increases via scattering or with larger incidence angle θ d) UV-C dosage is attenuated as light enters the inner layers of the N95 mask fabric, due to the effects of mask curvature on light attenuation orientations per lamp position. Masks positioned a distance R away from the light 61 source receive an ultraviolet dose reduced by a factor of 1/R 2 at their surface.
For a given segment of a mask on the treatment rack, the angle of incidence of each 63 light ray entering the fabric is cos(θ) = L · M where L is the unit light-vector from the 64 tube section to the mask segment, and M is the segment unit normal vector. The 65 density of light on the fabric decreases with distance R, but the attenuation of light as 66 it travels within the porous mask fabric is much more significant, and this loss is 67 enhanced with larger θ as the path length increases. We assumed the index of refraction 68 of the mask n ≈ 1.5 [11] and included surface reflection and refraction of transmitted 69 rays described by Snell's law [12] , which describes θ t , the transmitted angle using the 70 relation sin(θ) = n sin(θ t ). Light is attenuated exponentially as it passes through the 71 multiple layers of the fabric, and the energy density at depth x inside the mask segment 72 is the sum of components [13] :
where for the light ray i originating from lamp tube j, I ij 0 cos(θ ij ) are the energy 74 density just inside the mask and normal to its surface, θ ij are the angle of incidence, θ ij
October 30, 2020 3/8 . CC-BY-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.
The copyright holder for this preprint this version posted November 4, 2020. ; https://doi.org/10.1101/2020.10.30.20223354 doi: medRxiv preprint are the transmitted angles, and λ is a material characteristic decay length. We 76 determined λ, assumed to be constant in the fabric, through experiments at θ = 0 with 77 and without the mask fabric.
The internal intensity is the sum of all rays, including exposures from multiple lamps 79 or lamp positions. Masks placed at some locations have receive more or less treatment 80 due to the relative strengths and decay (attenuation and scatter) of these rays. Data 81 deposition: code used for simulation will be available from the GitHub repository 82 (https://github.com/PettigrewLab/N95Simulation.git) upon article publication.
Optimization 84 We considered mask treatment at each point of the array where a mask could be placed. 85 This involved simulated exposure along a 3M N95 mask's largest cross-sectional profile, 86 assuming quadratic curvature. In Fig 1 these values are reduced to a single pixel by 87 taking the minimum along this cross-section, while the full profile is presented in Fig 2. 88 As a baseline, we consider a simple protocol for these figures, where the masks are shows that the simpler arrangement does not treat N95 masks effectively, and would 101 require infeasible exposure times to treat masks along the entire array. Portions of 102 masks at every position received less than even a single-decimation dosage of 2 mJ/cm 2 , 103 with some surfaces not exposed directly due to mask curvature. In an optimized 104 protocol, however, adequate decontamination can be achieved by using our lamps for 105 15 minutes at each of the two optimized paired positions along the array (Fig 2) . In 106 contrast, flat folded masks can be effectively treated even with the simple protocol, with 107 masks on over 87% of the array receiving the desired dose throughout their entirety. 108 The way in which the simple protocol fails for curved masks is illustrated in Fig 3, in 109 which simulated treatment dosage within individual masks is displayed. When the 110 masks are exposed to light from only a single direction on each side, there is an order of 111 magnitude more variance UV-C dosage throughout the mask volume. Masks positioned 112 at extreme angles receive very unequal exposure and some parts may only be 113 illuminated on one side. Optimized exposure from two directions leads to a much more 114 uniform dose. At lateral lamp positions of ±91 cm, placed a longitudinal distance 52 cm 115 from the array, a 2x2 lamp protocol is optimal and requires about 15 minutes exposure 116 per lamp, or about 30 minutes total with two robots.
For masks that cannot be flattened, the attenuation becomes more important with 119 larger angles of incidence, and largely determines the necessary irradiation time, which 120
October 30, 2020 4/8 . CC-BY-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.
The copyright holder for this preprint this version posted November 4, 2020. illuminating both the front and back, one side or surface of a curved mask which is 131 illuminated obliquely can limit treatment effectiveness (Fig 2) . However, exposure from 132 multiple angles mitigates imbalance and is ultimately more efficient than longer October 30, 2020 6/8 . CC-BY-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.
The copyright holder for this preprint this version posted November 4, 2020. ; https://doi.org/10.1101/2020.10.30.20223354 doi: medRxiv preprint critical to know the minimum dose being delivered to each portion of the mask which 139 may be contaminated. We found that, throughout the full mask material, the delivered 140 dose distribution for any single mask showed a large variance, differing by more than 141 100x. This is primarily due to the curvature and difference in incident light path lengths 142 for locations across the mask when illuminated from a single source on both sides 143 (Fig 3) . Increasing the number of exposure angles is an efficient way of lowering the 144 total treatment time, and using the optimized configuration with two positions on each 145 sides of the mask reduces dosage variance to ≈ 2.5x (Fig 1) . There are diminishing 146 returns from using 3 paired locations, with only slightly greater uniformity and 147 efficiency at this array size.
Re-using masks helps to mitigate potential dangerous PPE shortages that would 149 leave clinicians and communities vulnerable to a viral pandemic. UV-C sterilization 150 using multiple angle exposures to ensure mask safety is a feasible option for the many 151 hospitals across the world that already have mobile UV-C systems. Hundreds of these 152 masks can be processed in a day with a single suspension system. However, care should 153 be taken to ensure sanitization of the mask interior layers, which is highly sensitive to 154 mask curvature and has been neglected in previous work. Implementation of properly 155 designed protocols could prevent the need for additional capital investment from 156 hospitals already incurring reduced revenue and increased expenses. 