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Respirator Filtration Efficiency Calculator

Catalog of Regulatory Science Tools to Help Assess New Medical Devices 

The Respirator Filtration Efficiency Calculator is a conservative computational tool that assists stakeholders with the assessment of personal protective equipment (PPE) textile materials, namely respirator / mask materials, to estimate particle filtration efficiencies compared with those of a reference surgical N95® respirator.

Technical Description

This computational tool enables users to input microstructural parameters of respirator fabrics to estimate personal protective equipment (PPE) filtration efficiency as compared to a reference surgical N95® respirator.  It uses mass transport equations to calculate filtration efficiency of a respirator filtration material based on three material characteristics obtained via scanning electron microscopy (SEM) imaging: fiber diameter, material layer thickness, and packing density. From these parameters, the computational tool can determine a conservative log10 reduction in particle-penetration across a particle size range, an overall filtration efficiency (OFE), and a comparison of the results of the test material OFE with those of a surgical N95® respirator.

N95® and other respirator PPE are constructed from nonwoven fabrics [1-4]. Particles may be filtered by fibers by way of diffusive, interceptive, impactive, electrostatic, gravitational, inertial and/or other mechanisms [1]. The physics-based computational model presented in this tool incorporates the dominant mechanical capture modes of diffusive, interceptive, impactive, and the combination of diffusive and interceptive to determine filtration efficiency [1,3,4]. The model consists of a set of constitutive equations that depend on the measurable filter properties of material thickness, material fiber packing density, and mean fiber diameter [1]. The distribution of these properties is used in a Monte Carlo simulation to provide a distribution of filtration efficiencies.

A graphical user interface (GUI) takes the means and standard deviations of fiber diameter (df), packing density (α), and thickness (L) measurements as inputs. The GUI outputs the performance of the user’s product in the form of violin plots, which display the distribution of the predicted log10 reduction of particle penetration. A numerical table is provided for the log10 reduction at the 95th, 75th, 50th, 25th, and 5th percentiles for specified particle size ranges. Additionally, in the violin plots the user’s product is compared with a reference surgical N95® respirator at different particle size ranges. The tool determines statistical significance using a one-sided Mann-Whitney U test (p = 0.05); i.e., if the user’s product has significantly worse performance than the reference (p<0.05), the violin plot is shown in red, but if the performance is comparable or better than the reference (p≥0.05), the violin plot is shown in green.

Intended Purpose

The intended purpose of this calculator tool is for rapid, preliminary estimation of filtration efficiency for surgical masks and N95® respirator materials. This tool is intended to facilitate comparison of a respirator or mask material’s filtration efficiency with that of a reference surgical N95® respirator to reduce or complement some labor-intensive testing some labor-intensive testing. This RST may be used to inform and expedite decisions around the design, manufacture, use, or potential re-use of surgical N95® respirator materials. These applications are limited to assessments informed by microstructural characteristics. All applicable regulatory requirements remain in effect.

The calculator is not intended to substitute for any current regulatory requirements around N95® respirators. As a reference only, users may compare calculator outputs to data obtained using bacterial filtration efficiency (BFE) testing per ASTM F2101-23. We describe how this computational model complements BFE testing per ASTM F2101-23 by providing stratified particle-size analysis.  The current ASTM standard uses an Andersen Impactor* instrument with viable Staphylococcus aureus (S. aureus) organisms, along with an equation provided in the ASTM standard that calculates BFE based on the percentage of filtered organisms across all size ranges. The Andersen Impactor is used to examine the presence of particles within a range of +7 µm to 0.65 µm [5]. The sampling system consists of six stages, and each stage tests for a different, successively smaller particle size range. Stages five and six collect particles from 2.1 µm – 0.65 µm [5]. Surgical N95® respirators must be capable of filtering out 95% of the particle-sizes captured in stages five and six, per Code of Federal Regulations 42 CFR Part 84.170.

Because the BFE test using the equation from ASTM F2101-23 averages filtration results over

all the Andersen Impactor stages, a respirator that fails to filter the most critical sizes < 2.2 µm may appear to pass the averaged BFE test. This RST calculator tool allows assessment of filtration at stratified particle size ranges corresponding to respective Andersen Impactor stages, which provides a more nuanced estimate of the filtration efficiency, even in the critical size range of < 2.2 µm.

Testing

Comparison to ASTM F2101-23

Four different commercially available surgical N95® respirator products were purchased from commercial sources. These surgical respirator products were previously approved by CDC/NIOSH-NPPTL and cleared by FDA. A commercially available mask not cleared as a surgical N95® respirator served as a negative control for filtering critical particle size ranges < 2.2 µm (i.e., the mask does not filter particles of this size range). The respirators and the mask were each tested with triplicate biological samples (n=3), and bacterial filtration efficiency (BFE) was calculated for each product using the equation provided in ASTM F2101-23. The results for all four surgical N95® respirator types and the mask, which serves as a negative control for filtering particle sizes <2.2 µm, demonstrated BFE above 95% (“passing”) according to ASTM F2101-23, showing a limitation of the ASTM method for critical particle size ranges < 2.2 µm.

The fibrous microstructures of respirator and mask filter layers were imaged via SEM. Analysis by ImageJ yielded ranges of values for measurements of fiber diameter, two-dimensional porosity (negative space) from which packing density was calculated, and thickness of the filter layer for each type of respirator. The mean fiber diameters for the surgical N95® respirators fell into a tight range, with the non-regulated mask demonstrating the smallest mean fiber diameter. The most variable property measured among respirators was thickness.

Using the Respirator Filtration Efficiency Calculator tool, the negative control mask fails in performance when compared to a surgical N95® respirator, thereby showing the benefit of the present calculator tool for assessing filtration efficiency of the most critical particle size ranges. 

Computational Model

The computational model of the Respirator Filtration Efficiency Calculator was validated and analyzed for model sensitivity to the user input parameters by varying their values to examine their effect on the Overall Filtration Efficiency (OFE). Subsequently the Calculator tool was beta-tested for usability.

  • Model Validation: Metrics to assess the computational model performance were characterized using practices aligned with ASME V&V 40 (“Assessing Credibility of Computational Modeling through Verification and Validation: Application to Medical Devices”). The outcome of this evaluation is described in the manuscript provided in the supporting documentation.
  • Model Sensitivity Analysis: Model sensitivity was determined by comparing four parameters: fiber diameter, filter layer thickness, particle size, and material packing density. Specific values were maintained as constants: (1) the particle size ranges were kept as constant values (per comparison to Andersen Impactor stages 1-6) and (2) the packing density was kept as a constant, respective of each of the respirator types and mask.  The fiber diameter and filter layer thickness were varied to examine their effect on OFE. The combination of all four parameters was used to generate a table of corresponding overall filtration efficiencies as contour plots, found in the manuscript linked in the Supporting Documentation. The contour lines represent the 95% threshold per each respective packing density that corresponds to a given respirator or the mask.  From the graphic analysis, the resulting output from the model is conservative and predictive when compared with experimental results to assess OFE and filtration efficiency relative to specific particle-size ranges.

Beta Testing of GUI and Acquisition of Model Inputs

The goal of beta testing was to evaluate the user interface functionality of the Calculator Tool and to further verify the precision of the results of user data obtained from SEM micrographs. Five (5) beta testers of the GUI were given instructions on accessing the tool, as well as detailed instructions needed to obtain inputs for the tool from SEM micrographs, which are used to calculate an output. Beta testers were asked to download 3 test SEM files each for 2 products (for a total of 6 SEM files) and follow the procedures outlined in the files User Guide and Example use of ImageJ and DiameterJ for SEM measurements included in the supporting information below. Briefly, the steps are for the user to:

1) Use ImageJ and DiameterJ to measure material thickness and calculate packing density;

2) Use Image J and DiameterJ to examine SEM image meta information and create segmented images in preparation for fiber diameter analysis;

3) Use Microsoft Excel to filter DiameterJ output of segmented images and to extract fiber diameter means and standard deviations; 

4) Input mean fiber diameter results, material (layer) thickness, packing density, and their standard deviations measurements into the Respirator Filtration Efficiency Calculator;

5) View statistical results of filtration efficiency.

All beta testers were successful in generating values for input required by the calculator. The coefficient of variation (CV) in the mean fiber diameter between users in the beta test was less than 5% for both products evaluated. These values were small compared to the CV in the measured fiber diameter for each individual user and product (range:7-17%).  A two-tailed Student's t- test was performed to compare measured fiber diameters between users. All combinations were found to have  P-values greater than 0.05, and therefore there were no statistically significant differences. Based on this testing, differences from user to user are expected to be minimal under the conditions of the beta test, i.e. same images and adherence to the protocol outlined in the user guide.  

Limitations

  • The mechanisms of filtration considered by the calculator are diffusive, interceptive, impactive, and a combination of diffusive and interceptive. The calculator was validated using 4 different fibrous surgical N95® respirators and one mask. For products where additional or different mechanisms dominate, the tool may be less informative.
  • This calculator uses uniform distribution for particle size ranges. This calculator only takes into consideration particles sized 0.65µm to 10µm. Performance for particles outside of this range cannot be assessed using this tool.
  • The model was validated using 9 SEM images (three from each of the following critical-respiration areas: nose bridge, nostril, and mouth) from the filtration layer of 5 different products (45 SEM images in total); therefore, we recommend using at least 9 SEM images from the filtration layer for a given respirator when applying the tool. The SEM imaging parameters used are included in the manuscript provided in the supporting documentation.
  • SEM images were used in the characterization of the fiber diameters and material (filtration layer) thickness. Packing density was determined gravimetrically. While it is possible to use different characterization methods for these microstructural parameters, no alternative characterization methods have been evaluated as part of this RST. Users wishing to apply alternative methods should conduct their own validation. 
  • This calculator considers only the microstructural characteristics of fiber diameter, packing density, and filtration layer thickness. Other material parameters are not considered in the model.
  • The model was developed and validated using ImageJ (Fiji) v1.51. Results obtained with other versions of ImageJ (Fiji) may not be comparable to validated outputs. Users should verify software version compatibility before analysis.Images in which DiameterJ is unable to identify a fiber will cause a processing error within DiameterJ. If this occurs, the user will need to reload DiameterJ, restart the analysis from the beginning, and remove images that are too bleached or too black to identify a fiber. The Example Use of ImageJ and DiameterJ for SEM Measurements file (embedded below) provides a description on image selection appropriate for analysis and examples of those images that are likely to result in a processing error.
  • The output from the calculator is conservative by design, based on a 5% lower bound of the predicted outcomes. Therefore, filtration calculated by the model is generally expected to be less than the real-world performance. The tool is not intended to be predictive, but rather a comparative tool between a subject and reference respirator.

Supporting Documentation

  1. Bai, H., X.M. Qian, J.T. Fan, Y.L. Shi, Y.C. Duo, C.S. Guo et al.: Theoretical Model of Single Fiber Efficiency and the Effect of Microstructure on Fibrous Filtration Performance: A Review. Industrial & Engineering Chemistry Research 60(1): 3-36 (2021).
  2. Paul, D., A. Gupta, and A.K. Maurya: Exploring options for reprocessing of N95 Filtering Facepiece Respirators (N95-FFRs) amidst COVID-19 pandemic: A systematic review. Plos One 15(11)(2020).
  3. Avinash Patil, N., P. Macchindra Gore, D. Shanmugrajan, H. Patil, M. Kudav, and B. Kandasubramanian: Functionalized non-woven surfaces for combating the spread of the COVID-19 pandemic. Interface Focus 12(1): 20210040 (2022).
  4. Payet, S., D. Boulaud, G. Madelaine, and A. Renoux: Penetration and Pressure-Drop of a Hepa Filter during Loading with Submicron Liquid Particles. Journal of Aerosol Science 23(7): 723-735 (1992).
  5. Andersen, A.A.: New sampler for the collection, sizing, and enumeration of viable airborne particles. J Bacteriol 76(5): 471-484 (1958).

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