The effects of face mask specifications on work of breathing and particle filtration efficiency.

The outbreak of the ongoing coronavirus disease 2019 (COVID-19) pandemic has led to the recommended routine use of face masks to reduce exposure risk. In this study, the increase in work of breathing (WOB) imposed by face masks is theoretically studied for both normals and patients with obstructive and restrictive lung diseases at different levels of activity. The results show a significant increase in WOB due to face masks, which is more severe in higher activity levels. The added WOB is considerable during physical activity and may be intolerable for patients with preexisting lung disease and may contribute to inspiratory muscle fatigue and dyspnea. Moreover, in this study, the effects of the physical properties of a fibrous medium, including thickness, porosity, and fiber diameter, are analyzed on the particle filtration efficiency (PFE) and the added WOB. The relations between the physical properties of the fibrous medium and the added WOB and the PFE are shown on some contour plots as a quick and simple tool to select the desired physical properties for a single layer filter to ensure that the added WOB is comfortable while the PFE is sufficiently high.

pressure dropPa

pressure gradientPa.m−1

dynamic viscosity of the airPa.s

surface area of pore sectionm2

respiratory compliancem3.Pa−1

Cunningham slip correction factor-

diffusion coefficient of particlem2.s−1

fiber diameterm

particle diameterm

air flow ratem3.s−1

forchheimer coefficient-

permeability coefficientm2

boltzmann constantj.K−1

knudsen number of particle-

kuwabara hydrodynamic factor-

filter thicknessm

peclet number of particle-

interception parameter-

breathing frequencymin−1

particle Reynolds number-

respiratory resistancePa.s.m−3

stokes number-

absolute temperatureK

inspiration times

face velocitym.s−1

tidal volumem3

added WOB due to mask resistancej

solidity of the filter medium-

porosity of the filter medium-

PFE of the fibrous medium-

PFE of the single fiber due to adhesion-

PFE of the single fiber due to diffusion-

PFE of the single fiber-

PFE of the single fiber due to inertial impaction-

PFE of the single fiber due to interception-

mean free path of air moleculesm

density of the polypropylenekg.m−3

surface density of the filter mediumkg.m−2

dimension -less pressure drop-

Introduction

Since the emergence of the ongoing coronavirus disease 2019 (COVID-19) pandemic, the routine use of respiratory protective devices (RPDs) has been recommended to reduce exposure risk. Furthermore, the most recent recommendations of the World Health Organization include the wearing of face masks by the general public for mitigating the risk and impact of COVID-19. The most used RPDs among healthcare workers and the general population are surgical face masks (SMs) and filtering facepiece respirators (FFRs), especially N95 FFRs. The continual wearing of RPDs is crucial for personal protection from exposure to contaminated particles or the risk of respiratory infections. Although RPDs are mandatory and highly recommended for areas most affected by the COVID-19 pandemic, significant difficulties have been observed in RPD wearers because of physical symptoms and discomfort.

Major experimental studies have been performed on PRDs comfortability. Some researchers used automated breathing and metabolic simulators [1,2], while others tested the masks comfortability on human subjects [3,4]. Potential reasons for discomfort with masks include a high temperature in the mask cavity leading to thermal discomfort [3], [4], [5], [6], [7], [8], CO2 accumulation, decreased oxygen causing headaches while wearing N95 FFRs [1,6,9], and mechanical factors such as increased breathing resistance [2,4,6]. A recent study has shown that panic-prone individuals may be at higher risk of mask-related respiratory discomfort [10].

An increase in breathing resistance up to approximately 300% for N95 FFRs was previously reported [4]. The increased breathing resistance, in association with CO2 rebreathing while wearing masks, may amplify respiratory fatigue and impair physical work capacity [11]. However, no indications of increased respiratory effort at a low workload for a relatively brief period were observed by Roberge et al. [12]. Hopkins et al. reported that the pulmonary function and cardiopulmonary exercise capacity highly impaired by N95 FFRs in healthy individuals [13]. Later, Hopkins et al. found some flaws in their work which took the validity of the study into question [13]. The authors discussed that since there were no significant different results for arterial blood gasses, heart rate, cardiac output and blood pressure between masked and unmasked conditions, in no way should it serve as a recommendation for avoiding mask use during exercise. These different results suggest the use of a mathematical model to investigate the effect of workload level on the increased work of breathing (WOB).

There are various experimental researches in the context of particle filtration efficiency (PFE) of face masks [14], [15], [16]. Well-fitted respirators are required to achieve > 95% aerosol filtration under standard conditions. PFE depends on the filter material [17,18], the properties of the fibers, including structure, diameter and electrostatic charges [17,[19], [20], [21]], the number of layers [22], shape (surgical style, conical, or duckbill), and facial fit [17,23,24]. Moreover, a considerable reduction in PFE during a cyclic coughing incident has been observed [25]. Although the main mechanisms for aerosol penetration through the masks are well studied [26], the combined effects of physical properties of the fibrous medium (including fiber diameter, porosity, and thickness) and the wearer's level of activity on PFE are not reported.

This study computes the increase in WOB imposed by masks through a porous media model. Then, the effects of physical properties of the fibrous medium and the wearer's level of activity are investigated on the added WOB and the PFE.

Material and methods

The filter medium, made up of randomly-oriented fibers, was defined as a porous media to simulate its resistance to flow. Assuming an adequate fit condition, almost all inhaling air passes through the filter medium without leakage. In laminar flow through porous media, the pressure drop is proportional to velocity according to Darcy's law [27]:

In this equation, v is the face velocity, k is the permeability coefficient of the medium, and µ is the dynamic viscosity of the fluid (1.8e-5 Pa.s), and ∇P is the pressure gradient in the thickness of the medium, L.

The face velocity is the fluid velocity and is related to the fluid flow rate, f, through the Eq. (2).in which, A is the surface area of the filter medium. According to detailed physical properties found in the literature for classical surgical masks [28], we have found the solidity of surgical masks using Eq. (3).where ρSF is the surface density and ρ is the available density of the polypropylene [29]. So, the assumed porosity of the surgical mask, ε =1- α, is 0.71.

For N95 FFRs, we have used the previously reported values for the physical characteristics of the N95 3M8510 (FFR1) listed in Table 1 [30], while for the surgical mask such data were not available. For the surgical mask, the reported pressure drop were 2.667 ± 0.137 mmH2O with the KFDA protocol (constant flow rates of 30 l/min) [24]. Substitution into Eq. (1) gives the average air permeability of 4.84e-12 m2. The assumed surface area and thickness of surgical mask is 163 cm2 [31] and 0.234 mm [28], respectively.

Table 1

Physical characteristics of the N95 FFR1.

Layer	Thickness (mm)	Fiber diameter (µm)	Packing density (α)	Surface area(m2)
External	2.27	22.1	0.104	0.0163
Middle	1.77	5.4	0.096
Internal	0.36	15.4	0.101

According to the theoretical predictions of Spielman and Goren [32], dimensionless pressure drop, Φ, can be expressed by the following curve-fitted equation for the case in which all fibers are normal to flow direction.in which α is the solidity or packing density of the fiber medium. So, the permeability of each layer of the N95 FFR can be computed by Eq. (5).

The modified form of Darcy's equation is Forchheimer's equation that also considers the inertial effects (Eq. (6)) [33].where F is a dimensionless number called Forchheimer coefficient. Ergun suggested another form of Eq. (1) for granular materials expressed by Eq. (7)[34].in which g and d, are gravitational acceleration and fibers diameters, respectively.

According to Eq. (7), F can be expressed by Eq. (8).in which ε is the porosity of the fibrous medium. The fibrous masks have multiple layers of randomly nonwoven fibers that are not similar in shape to granular materials. However, there is a good agreement between the F coefficient of Ergun's equation and the numerical data on fibrous structures [34]. So, we have used Eq. (8) for the F coefficient.

In this study, four level of minute ventilation (15, 30, 60, and 85 l/min) were tested which covered the breathing flow rate range of an adult under different activities (rest, light, moderate and heavy activity).

Assuming a sinusoidal profile for the inspiratory flow rate, f = Vπ/(2t)sin (πt/t), the added work of breathing due to mask resistance is computed by Eq. (9)

In whichΔpis the pressure drop due to the mask substituted from the Eq. (6) and ti, and VT are the inspiration time and tidal volume, respectively. We have increased the respiratory rate, RR, by increasing the level of activity while I:E = 1:1.1 according to Table 2 [35].

Table 2

Breathing parameters assumed in different levels of activity.

	Rest	light activity	moderate activity	heavy activity
Minute ventilation (l/min)	15	30	60	85
RR (cycle/min)	15	25	30	35
VT (l)	1.00	1.20	2.00	2.43
ti (s)	1.80	1.08	0.90	0.77
Flow rate (l/s)	0.56	1.11	2.22	3.15

We have computed the basic WOB of the respiratory system by the following equation:in which Rrs, f, and Crs are the respiratory resistance, inspiratory flow rate, and respiratory compliance. The first term of Eq. (10) is the resistive work required to overcome the frictional resistance to airflow during breathing that occurs due to the resistance of different compartments of the respiratory system, i.e. lung airways, and pulmonary and chest wall tissue resistances.

We have compared the values of WOB for three types of lung mechanics, namely healthy, resistive, and obstructive. The compliance values for healthy and obstructive are considered to be 0.1 l/cmH2O, while it is assumed 0.05 l/cmH2O for restrictive lung mechanics. We have followed the previous approach to find respiratory resistance [36]. In this approach, some experimental constants were used for healthy and COPD individuals. The reported constants for COPD individuals are used for obstructive while the constants for both healthy and restrictive lung mechanics are the same.

The porosity and fiber diameter are two parameters that controls both breathability and PFE of the fibrous medium. Increasing the porosity of the fiber medium increase the breathability while could lower the PFE hence it is a double-edged sword.

The PFE may be predicted based on the following formula [37].where ηf is the single fiber efficiency due to inertial impaction, ηI, interception, ηR, diffusion, ηD, and adhesion, ηA given in Eq. (12).

In Table 3 , the relations for computing these filtration efficiencies by different mechanisms are expressed.

Table 3

Formulations of the PFE of a single fiber by different mechanisms; inertial impaction, diffusion and adhesion.

Inertial impaction	η_I=2R(1−α)Stkα+(1−α)αStk^2ku	[40]
Interception	η_R=1+R2ku(2ln(1+R)−1+α+(11+R)^2(1−α2)−α2(1+R)^2)	[41]
Diffusionz	ηD = 2.9Ku−1/3Pe−2/3 + 0.62 Pe−1	[42]
Adhesion	η_A=190(Re_p*Stk)^0.68+190	[43]
Governing parameters	R=d_pd_fStk=dp^2ρ_pCsv18μd_fku = −ln (α)/2 + α − α2/4 − 3/4Kn=2λd_pPe=v.d_fDD=k_BTC_s3πμd_pC_s=1+Kn(1.207+0.44exp(−0.78kn))Re_p=ρ_pd_pvμ

In addition to three main filtration mechanisms, inertial impaction, interception, and diffusion, we could take particle-fiber interaction into account, i.e., the particle rebound and re-entrainment. Eq. (12) calculate the single fiber efficiency based on collision efficiency (sum of collection efficiencies due to impaction, interception, and diffusion) multiplied by the collection efficiency due to adhesion effects [38,39]. According to the formulation of ηA, it is near unity for micron particles in breathing flow rates.

The effect of electrostatic charge of fibers on the filtration efficiency has not been considered in this study. However, the PFE of electret fibers is significantly higher than mechanical ones.

The effect of leakage flow

In order to consider the leakage flow through the face mask we assume that there is a small gap between mask and face (Fig. 1 ) [44].

Fig.1

Schematic of mask with face-seal leakage [44].

Assuming Darcy's law through the filter material of mask

Where vf is the face velocity of the filter. Flow through the gap can be described with Bernoulli's equation (neglecting the gravitation), with

Where vg is gap air velocity. Combining Eqs. (13) and (14) the relationship between vf and vg can be found, with

The inspiratory flow rate, f, is equal to the volumetric flow rate through the filter, ff, and the gap, fg. So,where Af and Ag are the surface area of the filter medium and gap. Substituting Eq. (15) into Eq. (16) yields

Therefore, vg can be found as below

It should be noted that this equation has two solutions but only the solution with positive sign is acceptable.

Defining a gap factor, σ=Ag/Af, one can find the leakage flow ratio, LR, as below

The normal gap area varies between 0 and 5% of the mask area [44]. We can assume that σ = 0.05 for SMs with large gap and σ = 0.02 for N95 FFRs with small gap.

The inspiratory flow rate, f, substituted in Eq. (8), should be multiplied by (1-LR) to consider the leak flow.

For the PFE calculation, we should also modify the previous PFE, η, as the following equation [44]

Results

Without leakage flow

The ratio of the second to the first term in the right-hand side of Eq. (6) is shown in Fig. 2 . According to Fig. 2, the ratio of the inertial to viscous pressure drop is not significant, even by increasing the flow rate or level of activity in the studied masks. The error caused by ignoring the F coefficient in estimating the pressure drop of the both types of masks is smaller than 1%.

Fig.2

The importance of considering F coefficient in pressure drop of face masks.

This study computes pressure drop, additional resistance, and WOB imposed on a healthy subject wearing both an SM and an N95 FFR, as shown in Table 4 .

Table 4

Effect of wearing surgical masks and N95 respirators without leakage on the pressure drop, resistance, and WOB at different levels of activity.

Surgical mask
Level of activity	Rest	Light	Moderate	Heavy
Pressure drop (cmH2O)	0.30	0.59	1.19	1.68
Added resistance (cmH2O.s/l)	0.53	0.53	0.53	0.54
Added resistance (%)	25.68	22.93	19.10	16.67
Added work of breathing (cmH2O.l)	0.37	0.88	2.95	5.08
Added work of breathing rate (J/min)	0.55	2.20	8.84	17.78
Added work of breathing rate (%)	3.87	5.25	5.52	5.70
N95 FFR
Level of activity	rest	light activity	moderate activity	heavy activity
Pressure drop - external layer (cmH2O)	0.07	0.14	0.28	0.40
Pressure drop - middle layer (cmH2O)	0.79	1.58	3.16	4.49
Pressure drop - internal layer (cmH2O)	0.02	0.04	0.09	0.12
Pressure drop (cmH2O)	0.88	1.77	3.54	5.01
Added resistance (cmH2O.s/l)	1.59	1.59	1.59	1.59
Added resistance (%)	76.37	68.22	56.83	49.62
Added work of breathing (cmH2O.l)	1.09	2.62	8.79	15.17
Added work of breathing rate (J/min)	1.64	6.56	26.36	53.11
Added work of breathing rate (%)	11.53	15.66	16.48	17.01

With leakage flow

Assuming that σ = 0.05 for SMs with large gap and σ = 0.02 for N95 FFRs with small gap, the leakage ratio, pressure drop, added resistance and WOB are expressed in the Table 5 for different level of activity.

Table 5

Effect of wearing surgical masks and N95 respirators with leakage on the pressure drop, resistance, and WOB at different levels of activity.

Surgical mask (σ = 0.05)
Level of activity	Rest	Light	Moderate	Heavy
LR	0.080	0.042	.022	0.016
Pressure drop (cmH2O)	0.27	0.57	1.16	1.66
Added resistance (%)	25.68	22.93	19.10	16.67
Added work of breathing rate (%)	3.28	4.82	5.28	5.52
N95 FFR (σ = 0.02)
Level of activity	rest	light activity	moderate activity	heavy activity
LR	0.042	0.022	0.011	0.008
Pressure drop (cmH2O)	0.85	1.73	3.50	4.97
Added resistance (%)	76.37	68.21	56.83	49.62
Added work of breathing rate (%)	10.57	14.98	16.11	16.74

As shown N95 in Table 5, the leakage ratio decreases by increasing inspiratory flow rate consistent with the results of previous research [45]. The comparison of the results in Tables 4 and 5 shows a maximum of 8% decrease in pressure drop and 15% decrease in added WOB under the leakage condition.

According to Table 5, SMs and N95 FFRs cause 0.27 and 0.85 cm H2O pressure drop at rest condition. For the surgical mask, the previously reported pressure drop were 2.667 ± 0.137 mm H2O with the KFDA protocol and 9.283 ± 1.087 mm H2O with the US NIOSH protocol [24]. These two protocols use constant flow rates of 30 and 85 l/min, while our studied flow rates are presented in Table 2. It means that the rest condition (0.56 l/s) is approximately equivalent to tested flow rate of KFDA protocol (30 l/min). Thus, our predicted pressure drop for SMs at rest condition (2.7 mm H2O) well agreed with the measured value at the corresponding flow rate (2.67 mm H2O).

At rest condition, the added resistance is about 25.68 and 76.37% of the healthy lung and the added WOB is about 3.87 and 11.53% of the healthy lung for SMs and N95 FFRs, respectively. The previously reported range for the added inspiratory resistance of N95 FFRs is up to approximately 300% [4,46]. Therefore, our simulation results are within the reasonable range.

In Table 6 , the basic values of WOB in the absence of the face mask are computed for subjects with three types of lung mechanics (healthy, obstructive lung disease, and restrictive lung disease). The basic WOB in the diseased lung is about 130–240% of that in the healthy lung and is higher in obstructive lung disease than restrictive lung disease. The total WOB while wearing a mask is shown in Fig. 3, Fig. 4 for healthy and diseased lungs. This increased WOB could be intolerable in patients.

Table 6

WOB rate (J/min) in three types of subjects with different lung mechanics at different levels of activity.

Level of activity	Rest	Light	Moderate	Heavy
Healthy lung	14.19	41.88	159.96	312.23
Obstructive lung diseases	22.95	79.13	358.32	795.79
Restrictive lung diseases	21.69	59.88	219.96	415.45

Fig. 3

WOB rate of healthy subjects and patients with obstructive or restrictive lung diseases wearing surgical masks.

Fig. 4

WOB rate of healthy subjects and patients with obstructive or restrictive lung diseases wearing N95 respirators.

PFE is calculated according to the formulation in the methods section for sodium chloride (used by NIOSH in certification testing of respirators [47]) with the most penetrating particle size (MMPS). The presently accepted MMPs for the mechanical filter (not electret filter) is 0.3 µm [29]. The PFE of external, middle, and internal layers of N95 FFRs for sodium chloride particles at the MPPS at the inhalation flow rate of 30 l/min is 16.99, 79.04, and 5.10%, respectively. Thus, the overall PFE of mechanical N95 FFRs for MPPS at 30 l/min is 1-(1–0.17)(1–0.79)(1–0.05) = 0.83. It is noteworthy that charging fibers in the respirators could increase the PFE of electret respirators above 95% [29].

To investigate the effect of porosity and fiber diameter on the performance of the masks, a one-layer fibrous medium with the known thickness (1, 2, and 3 mm) is assumed. This study computes resistive work imposed by the fibrous medium at rest condition through Eq. (9) for a wide range of porosity and fiber diameter. However, it is not enough because this study aims to keep the PFE above a critical threshold for MPPS. The PFE for different porosities and fiber diameters is computed through Eq. (11). Showing the contours of the added WOB and the PFE in the same plot, one can easily select appropriate ranges of porosity and fiber diameter with desirable added WOB and PFE values. The results are shown in Fig. 5, Fig. 6 for rest and light activity conditions, respectively. The results are shown for three different thicknesses of the fibrous medium (1, 2, and 3 mm).

Fig. 5

Added WOB rate (j/min) and PFE (%) for different porosities and fiber diameters in the rest condition assuming a fibrous medium with the thickness of (a) 1 mm, (b) 2 mm, (c) 3 mm.

Fig. 6

Added WOB rate (j/min) and PFE (%) for different porosities and fiber diameters in the light activity condition assuming a fibrous medium with the thickness of (a) 1 mm, (b) 2 mm, (c) 3 mm.

According to Figs. 5 and 6, to achieve the PFE of mechanical filters above 80% for MPPS, the red region above the line with a determined level of the added WOB is acceptable. As porosity increases, a smaller fiber diameter should be used to obtain the desired level of the PFE and the added WOB. Increasing fiber diameter in a fixed porosity lowers both the added WOB and the PFE. Similarly, increasing porosity in a fixed fiber diameter leads to higher breathability but lower PFE. Increasing the fibrous medium thickness leads to better PFE but lower breathability. According to Fig. 6, increasing the activity level reduces the PFE while increases the added WOB.

Discussion

For simplicity, this study assumes that air flows uniformly through the whole surface of the face mask, and there is a uniform pressure in the space between face and mask. However, it is not accurate because the maximum flow is generated just in front of the nose. Therefore, a fluid dynamic analysis for breathing through a face mask covering a human face is suggested as an improvement. Moreover, we have not computed the increase of pressure drop due to the clogging occurred by continuous usage of the face masks. This issue could also increase the added WOB of the wearers in the long durations.

According to Figs. 5 and 6, it is impossible to lower the added WOB while improving the PFE of a face mask by changing the fiber diameter, porosity, and the fibrous medium thickness. So, it is suggested to improve the PFE of the fibrous medium by other techniques such as electrical charging of the fibers.

Conclusions

This study examined the effects of face masks on the added resistive WOB of mask wearers at four different levels of physical activity. The added WOB at rest condition was about 3.5% and 11.6% of the healthy lung for SMs and N95 FFRs, respectively. While the body of literature reports that this issue is not significant for healthy individuals, the present study results suggested that face masks may increase WOB, even in healthy individuals during physical activity. Patients with preexisting lung diseases are more likely than healthy individuals to experience increased dyspnea while wearing a face mask due to the increased WOB above their tolerating threshold. This study estimated that using face masks for an extended period of time may increase pressure drop due to clogging.

The simultaneous effects of porosity, fiber diameter, and fibrous medium thickness of a fibrous medium were investigated theoretically on the added WOB and the PFE. Both porosity and fiber diameter can change the added WOB and PFE of face masks. By assuming a constant fiber diameter, a dilute filter with higher porosity has lower added WOB and PFE than a dense filter with lower porosity. Moreover, by assuming a constant porosity, an increase in fiber diameter results in lower added WOB and PFE. Changing the fibrous medium thickness is also a double-edged sword. Thicker filters have better PFE but higher added WOB. We presented these non-linear relations in some contour plots as a quick and simple tool to select the desired values of porosity and fiber diameter in the fibrous medium to ensure that the added WOB is comfortable while the PFE is sufficiently high (Eqs. (4), (17)–(20)).

CRediT authorship contribution statement

Mojdeh Monjezi: Conceptualization, Methodology, Writing – original draft. Hamidreza Jamaati: Supervision, Writing – review & editing.