Light propagation within N95 Filtered Face Respirators: A simulation study for UVC decontamination

This study presents numerical simulations of UVC light propagation through seven different filtered face respirators (FFR) to determine their suitability for UV germicidal inactivation (UVGI). UV propagation was modelled using the FullMonte program for two external light illuminations. The optical properties of the dominant three layers were determined using the inverse adding doubling method. The resulting fluence rate volume histograms and the lowest fluence rate recorded in the modelled volume, sometimes in the nW cm-2, provide feedback on a respirator's suitability for UVGI and the required exposure time for a given light source. While UVGI can present an economical approach to extend an FFR's useable lifetime, it requires careful optimization of the illumination setup and selection of appropriate respirators.

This study presents numerical simulations of UVC light propagation through seven different filtered face respirators (FFR) to determine their suitability for UV germicidal inactivation (UVGI). UV propagation was modelled using the FullMonte program for two external light illuminations. The optical properties of the dominant three layers were determined using the inverse adding doubling method. The resulting fluence rate volume histograms and the lowest fluence rate recorded in the modelled volume, sometimes in the nW cm -2 , provide feedback on a respirator's suitability for UVGI and the required exposure time for a given light source. While UVGI can present an economical approach to extend an FFR's useable lifetime, it requires careful optimization of the illumination setup and selection of appropriate respirators.

| INTRODUCTION
Rapid local or global outbreaks of disease, such as SARS, Ebola and COVID-19 caused by SARS-CoV-2, cannot be forecast despite the general knowledge that they will sporadically occur. Health care providers are particularly at risk during such outbreaks. For example, out of the 8096 reported cases during the 2002-2004 SARS outbreak, 1706 (21%) were health care workers [1], as were 221 of the 3956 fatalities in Sierra Leone during the 2019-2020 Ebola outbreak [2]. The death rate associated with SARS-CoV-2 induced COVID-19 ranges from 1.3% (Russia) to 15.5% (France) June 8 th , 2020 [3] and an average mortality rate of 3.7%, underscoring the need for a very high level of protection for health care workers. Hence, the use of N95 disposable filtering facepiece respirators (FFR) is restricted to front line health care professionals in most North American jurisdictions. Regular face masks are recommended for the broader public to reduce the infection rate further.
The current COVID-19 pandemic has severely stressed supplies of personal protective equipment (PPE), including N95 filtering facepiece respirators (N95 FFRs). In response, healthcare facilities worldwide are forced to extend the use or reuse of their N95 FFRs [4]. Few options can be adopted for N95 FFR reuse. The US Food and Drug Administration (FDA) Emergency Use Authorization (EUA) guidance states that vaporized hydrogen peroxide gas plasma or hydrogen peroxide vapour (HPV) can be used for FFR decontamination if various conditions are satisfied, such as being free of visible damage and visual soil/contamination [5]. Due to post-processing form loss, vaporized hydrogen peroxide gas sterilization is not authorized for use with respirators containing cellulose-based or paper materials. Moreover, these techniques are not readily available in some middle-and low-income countries. Among the alternative techniques, ultraviolet light germicidal irradiation (UVGI) is promising and is recommended by the US Centers for Disease Control and Prevention (CDC) [6].
UVGI-based viral deactivation is an easy-to-use solution, and its efficacy on N95 respirators has been confirmed by several studies [7,8]. For example, some groups have previously investigated the use of the UVC emission available in biosafety cabinets for these tasks [9,10]. Some FFR manufacturers have also provided their decontamination guidelines [11]. According to recent reviews, a minimum radiant exposure of 1 J·cm -2 is required for a consistent 3 log reduction in H1N1 or MS2 viral load [12]. However, a higher UV dose might be needed to achieve ≥3 log reduction of a non-enveloped virus, such as the more resistant adenoviruses, to obtain the EUA from the FDA as per their guidance [13]. FFR surface sterilization of more than 6 log inactivation for SARS-CoV-1 was reported for radiant exposures ranging from 600 mJ cm -2 to 3614.4 mJ cm -2 depending on the viral strain used [14,15]. UVGI decontamination does not appear to influence the performance of the respirator, even after repeated UVC exposure [16,17]. Lindsley et al. [17] demonstrated for 1860 and 9210 3M respirators no change in flow resistance or filter burst strength at radiant exposures up to 120 J·cm -2 , representing perhaps over 100 simulated disinfection cycles. Strap integrity remains an issue at higher radiant exposures, however, in practice, it is unlikely that N95 masks would be disinfected more than five times due to commonly-observed loss of fit at that point, given simple wear, independent of the disinfection process.
There are several knowledge gaps regarding N95 respirator decontamination using UVGI. A knowledge gap pertains to the understanding of light penetration through the fabric layers within the respirators. Previous studies did not provide a microscopic resolution of the diffuse fluence, , [mJ cm -2 ] within the masks. We consider this to be important as it can help estimate the inactivation of the virus within the respirator. Some trapped viruses in the respirator, if not inactivated, might be redistributed and re-aerosolized under conditions simulating those found in healthcare settings under moderate breathing [18]. Another gap is the effect of the UV wavelength on the decontamination performance, as most previous studies have focused on only 254 nm, which is emitted by traditional mercury arc-discharge lamps. Newer UV-LED systems can emit UV from 265 nm to 300 nm.
Here, we present a quantification of the optical absorption and light scattering coefficients for each layer of seven common FFRs, along with Monte Carlo-based modelling of light attenuation for multiple illumination schemes across the 250 to 300 nm range. Simulations were executed to determine the fluence rate-volume-histograms (FVH) across the multiple FFR layers. These experiments highlight the differences of the irradiance [mW cm -2 ] incident to the respirator surface and the resulting fluence-rate, Φ [mW cm -2 ], inside the respirator's fabrics. Irradiance is measured only over one hemisphere, whereas Φ is omnidirectional.
The 3M 1805 FFR contains cellulose and is therefore not suitable for hydrogen peroxide-based decontamination. The 3M 1860 and 1870 FFRs do not contain cellulose knowingly; however, they are not certified cellulose-free. Nevertheless, the 1860 model is approved for HPV decontamination. The FFR design is commonly comprised of polyester-based materials for the outer and the inner shell, whereas the filter fabric is polypropylene.
For the determination of the optical properties, 50 mm square samples were cut from the respirator and separated into three layers; for the outside layer, one sample was collected without printing and one with the test on the front. Figure 1 shows the prepared samples.

| Determination of FFR material optical properties
Optical properties were determined based on the approach of Scott Prahls [19], by quantifying the diffuse transmission and diffuse reflections using a single 6-inch integrating sphere (Labsphere, North Sutton NH, USA) with 1.25 inch (31.75 mm) entry and sample ports. The sphere's surface reflectivity at 250nm and above was determined by exposing the side of All rights reserved. No reuse allowed without permission.
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The copyright holder for this preprint this version posted June 16, 2020. . https://doi.org/10.1101/2020.06.12.20129395 doi: medRxiv preprint the sphere with an open sample port and closed sample port as previously described [19,20]. The measured sphere reflectivity is shown in Supplementary Figure S1. Data below 250 nm is unreliable and were excluded from further analysis. The resulting spectra suggest absorption bands within the Spectralon material or contaminations that may have accumulated over time.
The detector port was fitted with an optical fibre detector equipped with a cosine corrector (CC-3-UV, Ocean Optics, Rochester, NY, USA) and connected to a UV/VIS spectrophotometer (USB4F04880, Ocean Optics, Rochester, NY, USA) providing a spectral resolution of ~0.5 nm. Integration time was set to 6 secs, and 8 spectra were integrated with boxcar smoothing of 2. While the long integration time resulted in PDA saturation at λ> 400 nm, no blooming was evident at the shorter wavelength of interest. Spectral collection and readout were performed with an Ocean Optics SpectraSuite software.
A medium pressure mercury lamp with collimator was used as the light source (Model: PS1-1-120, Calgon Carbon Corp., Moon Township, PA). The light beam was apertured to 17 mm before the integrating sphere's entry port. Figure 2 shows an image of the physics setup. Background corrected transmission and reflection spectra were converted into diffuse transmission and reflection spectra. To apply the Inverse Adding-Doubling algorithm to extract the wavelength resolved absorption and reduced scattering coefficients [mm -1 ], the integrating sphere's surface reflectivity needed to be determined [20]. The reflectivity was determined through off-axis measurements as proposed [21]. As the outer filter and inner respirator layer thicknesses cannot be accurately measured, they were assumed to be 1 mm thick. Hence, the absorption and scattering coefficients are based on this thickness. This implied that the optical properties needed to be scaled prior to modelling the photon distributions inside the respirators and fluence-ratevolume-histograms need to be given only in % volume rather than absolute volume.
Both the Inverse Adding-Doubling algorithm and the Monte Carlo simulations require the assignment of an average refractive index for each fabric layer [22], comprised of the textile fibres and air. The refractive index of polyester, a birefringent material, is given as 1.71 to 1.73 along the fibres and 1.53 to 1.54 perpendicular to them. The fabric density of Dacron® is 1.38 g cm -3 . The initial photon incidence is perpendicular to the fibre axis. The mean flow pore diameters are estimated at 4-5 µm resulting in a packing density of 70% air volume. Hence, an average refractive index of 1.3 was assigned.
Polypropylene isotactic has a density of 0.91 g cm -3 and a refractive index of 1.492 with a fibre diameter of 1.2 µm. The mean flow pore diameter for non-thermal bonded fabrics is 1-500 microns but is reduced to 10-15 microns by thermal calendaring [23]. Again, the overall fabric density is low, and an average refractive index of 1.15 was assigned.

| Monte Carlo based light propagation in FFR
To predict the minimum UVC fluence rate, Φ, at any point in an FFR, Monte Carlo based in-silico photon propagation simulations were performed. Simulations were based on a standard 3D phantom fitted with the optical fabric properties derived above. Figure 3 shows an image of the hemispherical 3D phantom with an outer radius of 12 cm, comprised of the three layers, with 0.98, 1.77 and 1.05 mm representing the outer, filter and inner layer, respectively. The three-layer volumes are 24.84 cm 3 , 42.55 cm 3 and 24.34 cm 3 , each divided into 129550, 118565 and 99801 elements. The average tetrahedral size per layer was 0.192 µm 3 , 0.358 µm 3 and 0.841 µm 3 , accordingly.
Three 1, 3, and 5 mm broad light-absorbing stripes were added to investigate the effect of the black printing on the fluencerate inside the respirator. Additionally, a 5 mm wide and 2 mm thick object, simulating an aluminium nose piece, was added to the side of the hemisphere. In the 1 st set of simulations (A), illumination is via the outer shell with the respirators sitting supinely on an aluminium reflector and in the 2 nd set (B), illumination is via the inner layer with the FFR prone on the aluminium reflector. The absorption and reduced scattering coefficient of the aluminium pieces were 1 mm -1 and 20 mm -1 , respectively, allowing for a high backscattering albedo.
Two sources were modelled. A large flat circular source of 12 cm diameter and centred 10 cm over the respirator's apex when positioned supine and emitting normal to its surface simulated a very distant source. The second source represents a small 1 cm diameter photon emitting surface with a numerical aperture (NA) of 0.4 or 0.54, situated 10 cm over the supine or prone All rights reserved. No reuse allowed without permission.
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The copyright holder for this preprint this version posted June 16, 2020. . https://doi.org/10.1101/2020.06.12.20129395 doi: medRxiv preprint positioned respirator, respectively. To reduce the execution time of FullMonte simulations, the light sources were modelled as objects with photons emitted randomly over their surface triangles, either normal to the surface or within a userdefined solid angle [24]. 10 8 photon packets were launched in the FullMonte simulations [25], requiring less than 2 minutes, on an Intel(R) Xeon(R) CPU E5-2650 v4 running at 2.20 GHz equipped with 128 GB RAM when executing two threads on each of the 12 CPU cores. All sources were assumed to emit an irradiance of 1 mW cm -2 at their surface. The emitted photon packets were set to stand for the total power emitted per source. The simulation run times per source, wavelength, and FFR were < 120 sec after final source optimization.
For the generation of the fluence-rate-volume-histograms (FVH), the photon weight absorbed by each volume element is corrected of its particular volume and converted to a local Φ (r), followed by sorting the elements in descending order of fluence-rate and plotted versus volume [%].

| RESULTS AND DISCUSSION
While various recent studies reported on surface irradiation variations on N95 FFR [26] or transmission of select wavelengths through the different respirator layer material [6], the reports were only for perpendicular illumination. These models considered only light absorption properties of the filtering fabrics rather than absorption and light scattering properties to achieve complete 3D UVC light, propagation models. The latter is required to determine the minimum available Φmin within a respirator and has not been reported at this time. This is due to the unknown optical properties of the different polyester, polypropylene, and cellulose fabrics utilized in the manufacturing processes and lack of suitable simulation platforms for light propagation emitting from large extended sources to the highly light-scattering materials.
While the fabrics comprise micron-sized fibres with varying degrees of packing densities, light propagation simulations such as FullMonte most often assume bulk optical properties. Here, the program also assumes isotropic optical properties and does not consider birefringent properties present in polyester fibres. Figure S2 shows an example of the spectral conversions from raw spectra to fabric layer-specific diffuse transmittance and reflectance for the 3M 1860 and 9105s respirators.
Certain assumptions were made in determining the fabrics' optical properties for the Monte Carlo simulation. When determining the integrating sphere's reflectivity, the unknown reflection standard was iteratively changed until it was very close to the derived sphere reflectivity. Modulations of the sphere reflectivity due to potential absorption bands were not considered. The refractive index assigned to the outer shell and inner lining, as well as the filter materials, are estimates based on the fibre material and its packing density. The resulting layer-specific transmission values for the 1860 and 1870 respirators compare well to those determined using an actinometer-based technique (Dr Benoit Barbeau, Ecole Polytech Montreal, QB, Canada) and for data reported by Fisher et al. for 1860, 1870, and 8210 respirators. The absorption properties of the polyester and polypropylene have been determined previously. Polyester has a flat absorption in the UVA to the UVC region. However, there is a significant increase in absorbance below 245 nm. Polypropylene has considerable absorbance below 400 nm, albeit with little spectral shape. No sharp spectral absorption changes were seen in the 250 to 300 nm spectral range in our experiments. However, different materials have very different absorption coefficients as anticipated between polyester (low µa) and polypropylene (high µa).
Fabric fibres have a very high aspect ratio (>> 3.5), and their diameter is large compared to the wavelength of interest, and hence there aren't large variations in the scattering coefficient. The scattering coefficient varies little once the form factor, ρ, is > 10. [27,28] Based on a textile fibre diameter of 1.2 µm, ρ falls from 16.47 to 14.88 between 254 nm and 290 nm, respectively. This restricts the range for the scattering All rights reserved. No reuse allowed without permission.
(which was not certified by peer review) is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.   Fluence-rate-volume-histograms were plotted for the dual photon sources, large collimated ( Figure 5) and small divergent ( Figure 6) emitting 254 nm, and the two illumination directions via the outer and the inner shells respectively, and for the combined illumination of an FFR 3M 1860 and the 3M 9105s FFRs at all four wavelengths. The FVHs for all 7 FFRs at the four simulated wavelengths are available online; see Data Availability Statement at the end of the manuscript. The FVH in Figures 5 and 6, two top rows, show that single side irradiation will not achieve complete volumetric decontamination.
Not all tetrahedral received any photon-weight after launching 10 8 photon-packets. Hence, the minimum required irradiance for 100% of the FFR volume was 0 for both the large and small source models. While a higher photon-packet number would provide for non-zero values in all tetrahedral, the resulting fluence-rates would remain in the sub nW cm -2 range.
For a nominal source emission of 1 mW cm -1 , the lowest fluence rate, Φ, at 99% or 95% of the FFR volume following the combined illumination via outer and inner shell for the four simulated wavelengths, are summarized in Tables 1 and 2,  respectively. Repeat simulations, n=3, for 1805 and 9105s FFRs, resulted in standard errors < 1 % for Φmin > 0.25 µW cm -2 .
Manufactured printing on the outer shell layer does not influence the overall decontamination of the respirator due to the small added absorption relative to the fabric's absorption in the ultraviolet region of the optical spectrum. However, personalization of FFRs with Sharpies and other penetrating ink-based markers needs to be avoided, as are cosmetic cremes and lipsticks. Considering a 10 v/v% contamination of the outer layer with patient saliva or the inner layer with the bearer's saliva would increase the absorption coefficient by 0.085 mm -1 (Prof. Benoit Barbeau, Polytechnique Montreal, personal communication), comparable to the printing on the front shell, and thus would not impact the light distribution significantly.
The aluminium nose bridge did not cause significant shadowing effects for the simulated illuminations as it was not perpendicular to the direction of incidence. However, when light sources are coming sideways, significant shadowing will occur, possibly preventing the achievement of FDA guideline decontamination. There are substantial differences in the light scattering and absorption properties between the fabrics.
Using a small light source is not desirable as excessively long treatment times are required to achieve the required fluence, , over at least 99% of some FFRs' volume for UVGI. The difference in the determined Φmin between the sources is partially due to the 144 times higher power emitted by the large source.    (which was not certified by peer review) is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.  However, the higher irradiance alone does not explain the lower Φ in some volume elements of the hemisphere. The low Φ is due to a partial surface shielding of the FFR by its form and shallow incidence angles of the photons, see Figure 2. The steep decline of the FVH towards 100% of the volume can also be an artefact of the limited photons launched; however, the All rights reserved. No reuse allowed without permission.
(which was not certified by peer review) 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 June 16, 2020. . https://doi.org/10.1101/2020.06.12.20129395 doi: medRxiv preprint graphs suggest that a two order of magnitude increase in photon-packets would be required to overcome this limitation. Conversely, the 99% data is reliable as sufficient absorption events were recorded. The influence of the tissue optical property uncertainty is limited. Increasing µs by 10% in all three layers did not affect the Φmin shown in Tables 1 and 2 for the 3M 1805 FFR and reduced Φmin between 4.5% and 5.3% for the 3M 9105s FFR.
The required irradiation times, t, required to achieve a minimum fluence, , for UVGI of SARS-CoV-2 or other targets as required to achieve complete volumetric inactivation is calculated by = (ΦP) ⁄ , with P representing the irradiance in the mask plane. For example, to reach 65 mJ cm -2 for MS2 inactivation [29] by a large collimated source emitting 1 mW cm 2 of 254 nm would require over 32 times longer for a 3M 1860 FFR than a 3M 9105s. The computed UVC exposure times are very long for the modelled light source. They can be significantly reduced by optimizing the shape and position of the light source for a given FFR shape, Duckbill versus parabolic, utilizing available inverse optimization algorithms [30].
Given the textiles used in the various FFRs and their optical properties in the 250 to 300 nm range, renders them suitable, to various degrees, for UVGI, whereas others are not suitable.
The suitability of FFRs for UVGI varies widely for 4 of the tested models. Suitable M3 models include 1805, 1870+, 9210 and 9105s, where the latter would require the shortest illumination times. Three of the tested FFRs, 1860, 8110s and 8210, are less suitable for UVGI. Achieving the fluence-rate required for 6 log viral or bacterial inactivation, as currently defined by the FDA, over 100% of the respirators volume, results in an excessive irradiation time in these models, even for optimal light source placements. If only surface decontamination is desired as reported by some groups and be achieved in a much shorter time, however, the high photon absorption and scattering coefficient, pose serious challenges.
There are two shortcomings in the current study. First, the spatial resolution was limited to 0.2 to 0.8 µm 3, and it simulated only 3.5 10 5 tetrahedrals for the three layers combined. The current (June 10 th , 2020) Guidance for Industry and Food and Drug Administration Staff for EUA for PPE Decontamination [31] requires that greater than 6 log reduction of certain specified test organisms be demonstrated to allow a decontamination device to be approved for single person reuse of a mask. To demonstrate 6 log reduction using this model, simulation phantoms would need to contain > 10 6 tetrahedrals.
The second shortcoming is that the hemispherical shape and the small area that was illuminated represent a highly unlikely and worst-case scenario. In reality, UV fluence-rates would likely be one to two orders of magnitude higher since decontamination devices would be constructed to provide fairly uniform coverage of UV across the entire outer mask surface. However, the difference in FFR suitability for UVGI is not affected by either of these shortcomings, and each FFR model needs to be independently evaluated. Comparisons with actual biological experiments evaluating the complete volumetric decontamination of some of these FFRs are highly desirable.

| CONCLUSION
UVGI is a reasonable approach for FFR decontamination to extend a respirator's usable lifetime when supply chains are restricted during public health emergencies. Both the investment costs and environmental impact are low. Operator exposure to harmful UV radiation and ozone can be minimized by simple technical safety measures. However, to achieve consistent, fast and complete decontamination, the photonsource positions need to be paired to the respirator shape, and the optical properties of the FFR model to be irradiated needs to be determined at the UVGI wavelength, to establish the minimum required exposure time based on photon distribution simulations as described here. Figure S1 shows the diffuse reflectivity of the integrating sphere in the 250 to 350 nm range, and Table S1 lists the determined fabric optical properties, µa and µs', for three fabric layers of the seven evaluated FFRs at 254, 265, 280 and 290 nm.