Respiration mask waveguide optimisation for maximised speech intelligibility

The coronavirus disease (COVID-19) pandemic has highlighted global shortages of critical medical supplies, including personal protective equipment (PPE), ventilators, and essential medicines (Koven, 2020). Widespread transmission of the virus can be attributed to airborne particles and droplets, where PPE use is important to prevent viral transmission (Cook, 2020). Surgical facemasks and N95 respirators are accordingly used in healthcare settings worldwide; however, these masks are typically single-use, with disposable devices in high demand, and are typically constructed of non-biodegradable materials that have unmitigated environmental impacts (Prata et al., 2021). Moreover, commonly used surgical face masks were originally introduced only to protect patients from wound infection and contamination from surgeons (the wearer) during surgical procedures (Leung et al., 2020), and thus, have limited protective capacity in comparison to N95 (or similar) respirators (Chu et al., 2020). This is due in part to the poor face seal that is formed with the mask, limiting its effectiveness as PPE that can be used in a viral outbreak (Lockhart et al., 2020; Xu et al., 2021).

3D printing is an emerging alternative to address local face mask shortages, including at the onset of epidemics and in resource-poor or isolated environments lacking mask stockpiles. Some recent efforts using 3D printing have focused on creating reusable masks comprised of hard printable plastics, such as polylactic acid (PLA) and acrylonitrile butadiene styrene (ABS), in which a piece of filter material can be inserted (Tino et al., 2020). However, masks made from such materials are limited in their capacity to create a tight seal between the mask and users' face, diminishing their filtration effectiveness and comfort over long periods. An intermediate approach that spans the different mechanical properties required, namely, a stiff region containing the filter material and a more compliant one to interface with human skin, would combine off-the-shelf masks with 3D printed filtration components. The choice of the off-the-shelf mask component is important, with many designs based on full-face masks being overly cumbersome for continuous use. For example, a full-face snorkel mask was connected to a commercial filter in a 3D printed housing to create a reusable respiration mask (Greig et al., 2020; Kroo et al., 2020). Such approaches, however, should account for the ability to communicate effectively during their use, essential in clinical settings. Even conventional respiratory PPE, especially full-face or partial face masks, have been reported to reduce speech clarity and hence, communication efficiency (Johnson, 2016; Nickell et al., 2004; Palmiero et al., 2016; Radonovich et al., 2009; Schumacher et al., 2020). This effect is especially pronounced in noisy environments, frequently observed in busy hospital settings with sound levels in excess of 75 dB (Holmberg and Coon, 1999). Compounding the problem, the most comfortable materials (i.e., elastomeric ones) from which respirators are often made suffer the most in terms of speech intelligibility (Palmiero et al., 2016). The problem of poor speech intelligibility for respiratory protective equipment has previously been mitigated with passive and active communication systems. Passive measures include an integrated diaphragm or thin membrane that minimizes acoustic reflections (Ćirić et al., 2018; Rosert and Gdulla, 2001; Thompson et al., 2018), though this approach complicates device assembly, increases cost, and increases susceptibility to damage, contamination, and leaks. Active systems that amplify speech via a digital microphone and speaker have also been considered (Birli et al., 2007; Bloomfield, 1993; Parker and Richards, 1988; Skillicorn et al., 2003). For instance, wireless speech transmission was implemented for the (previously mentioned) full-face snorkel mask (Kroo et al., 2020). However, this similarly increases the cost, and reduces its robustness, limiting its widespread adoption.

In this work, we instead propose a numerical approach to mask topology optimisation to improve speech transmission. Here, rather than using any active (powered) methods or additional membrane components to facilitate acoustic propagation, we modify the shape of the mask features itself in order to maximise the frequency-selective transfer of acoustic energy between the interior and exterior of the mask volume. The technique is based on evaluations via the Speech Intelligibility Index (SII) to assess speech communication; here, in the context of a protective facemask that combines a compliant silicone off-the-shelf resuscitation mask with a custom 3D printed mask insert in which filter materials can be placed. The base resuscitation mask, used in clinical settings to administer oxygen and anaesthetic gasses to patients, forms an effective and compliant seal around the face, while the insert acts as an acoustic waveguide between the interior of the mask and the outside world to maximise the accumulation and transmission of acoustic energy [See Figs. 1(a)–1(c)]. In order to determine the waveguide topology that maximises SII, we employ a numerical routine that performs weighted multi-frequency band optimisation. The finalized acoustic waveguides, created for a range of different geometrical boundary condition constraints, effectively act as an “acoustic horn” to passively concentrate and direct acoustic energy (Kolbrek, 2008). This approach, taking into account the mask geometry itself and its effects on acoustic transmission, has implications for improving speech transmission in face masks, as well as maximising sound transmission between adjoining regions in general.

Speech communication can be evaluated via speech intelligibility measures, which are evaluated using perceptual methods or objective (technical) methods (Letowski and Scharine, 2017). Perceptional methods involve participants listening to identifying key words from natural or synthetic speech. One such method, the Modified Rhyme Test, has been previously employed to evaluate speech intelligibility of people wearing respiratory protection in medical settings (Radonovich et al., 2009). Perception-based tests, however, are difficult to meaningfully quantify and require large sample cohorts. Moreover, participant-based metrics are not an appropriate input for rapidly iterated numerical simulation.

In contrast to perception-based methods, objective methods use artificial signals comparable to average speech and algorithms for received signal processing while accounting for ambient noise. For example, Palmiero et al. used such an approach to experimentally assess speech transmission in protective facemasks and respirators commonly worn by healthcare workers (Palmiero et al., 2016). Because synthetic acoustic signals can be straightforwardly generated and evaluated, objective methods are generally more time-efficient, repeatable, and reproducible, making them suitable for numerical studies and rapid prototyping. In this work, we evaluate the system performance according to the Speech Intelligibility Index (SII) (ANSI S3. 5‐1997, 1997), valid for use with continuous noise sources, and which is highly correlated with perceptual and other objective tests (Letowski and Scharine, 2017; Samardzic, 2013). For speech intelligibility prediction, the index uses a weighted contribution of sound to noise ratio in individual frequency bands. The octave band SII is computed as the summation of band audibility function A_i multiplied by the band importance function I_i over octave central frequencies (250, 500, 1000, 2000, 4000, and 8000 Hz)

Lower (31, 63, and 125 Hz) and higher (16 000 Hz) frequencies have a minor impact on speech intelligibility and are, therefore, not reflected in the ANSI S3.5-1997. The band importance function $Ii$ indicates relative significance of a particular frequency band to speech intelligibility (see Table S1 of the supplementary material)¹. The band audibility function $Ai$ for the specified band is calculated from the speech $Ei$ and noise $Ni$ sound pressure levels (SPL, dB),

where this expression can take on values between 0 and 1. Since the sum of $Ii$ values over the six octave bands equals to one, the resulting SII value itself therefore ranges from 0 to 1, where a greater SII value reflects better intelligibility. In this study, the $Ei$ and $Ni$ values are evaluated independently as inputs to Eq. (2), with speech signal being recorded at 1 m in front of the sound source. Normal vocal effort speech spectra (⁠$Ein$⁠, Table S1) is the reference speech level without any mask sourced from ANSI S3.5–1997. The calculated speech level at the receiver is a function of the original speech level and the attenuating impact of mask materials, with

where insertion loss $ILi$ is the acquired SPL reduction due to the mask placement, $Eim$ and $Eib$ are the signals measured with and without the mask (superscript referring to mask and baseline, respectively), and $i$ represents the octave band index number in Table S1. To represent realistic conditions, a noise spectrum was added from an experimental study where time-averaged background sound pressure level (SPL) was measured in hospital environments (Kracht et al., 2007). In our calculations, we used the average spectrum from three separate operating rooms of The Johns Hopkins Hospital in Baltimore, Maryland (⁠$Ni$⁠, Table S1). Since SII does not account for fluctuating noises, the selected noise level represents continuous background noise in unoccupied rooms.

The numerical optimisation was performed in the COMSOL Multiphysics 5.5 simulation environment (COMSOL Multiphysics^® v. 5.6. www.comsol.com. COMSOL AB, Stockholm, Sweden). A two-dimensional model with axially symmetric boundary conditions along the centre axis was used to reduce computation time and permit rapidly iterated optimization. The model contained an air volume, head profile, mask, and waveguide, as shown in Fig. 2(a). Sound wave propagation in the air domain was simulated using the pressure acoustics module. The impact of elastic waves in the solid components were also accounted for using the solid mechanics module with mechanical damping. To compute the acoustic transmission, a frequency domain study was performed for each frequency band incorporating acoustic-structure boundary interaction. The face/head surface was simulated using an impedance boundary condition according to the impedance of human skin (0.45 MRayl; COMSOL Material library). The air domain is a sphere with 1 m radius to permit SII measurement at 1 m from the mouth. A spherical perfectly matched layer (PML) surrounding the air domain is imposed at the edge of the air domain to prevent reflections and given an accurate measure of the sound pressure level (SPL) at 1 m. To prevent reflections across the range of frequencies analysed, the thickness of the PML was equal to the wavelength (⁠$1.37 m$⁠) at the lowest frequency in this study (250 Hz). A port boundary condition was used to emit the sound. A preliminary simulation helped to calibrate the port output spectrum to maintain the reference speech level for the baseline (noise-free) voice in the absence of a mask. Air density (⁠$1.204 kg/m3$⁠) and speed of sound (⁠$343.2 m/s$⁠) were sourced from the COMSOL Material library. From the same module, we set the silicone density (⁠$1280 kg/m3$⁠), Young's modulus (4.16 MPa), and Poisson's ratio (0.0245). The silicone material structural loss factor (0.18) was employed from Guo et al., 2016. A comprehensive set of material data for polylactic acid (PLA) plastic, including density (⁠$1210 kg/m3$⁠), Young's modulus (2400 MPa), Poisson's ratio (0.42), and structural loss factor (0.025) was acquired from Rezgui et al., 2005.

Since the study domain has an axial symmetry, the 2D simulations represent external and internal parts with bell-shaped cross sections (with 2 mm thick walls) connected via a tube-like structure limited by the mask throat dimensions. The geometry of the waveguide elements inside the mask are similarly confined to the mask's internal extent, as measured from a physical Adult Silicone Mask 4–5⁺ (Laerdal Pty Ltd, Laerdal, Oakleigh, Australia, https://laerdal.com/au/item/870220). The external waveguide dimensions should also be limited so that they do not interfere with other PPE, such as face shields and goggles, whose imposed spatial constraint may vary according to the specific models of other PPE used. Moreover, while examination of the dynamics of gas flow through masks lies outside the (acoustics-focused) scope of this work, a large waveguide increases the respiratory dead space and breathing resistance. Thus, we implemented two different waveguide optimizations, both 70 mm in diameter but with either 36 or 20 mm long external parts (projecting outwards from the resuscitation mask).

Optimisation of waveguide elements was performed in order to enhance speech transmission. To do so, profiles of the internal and external parts of the waveguide were parametrized individually using six-point splines. The control points of each spline were distributed evenly along $z$-axis, whilst positions along the $r$-axis and tangent spline directions were design variables. Since SII is implied to be a speech intelligibility indicator, its value was an objective function in the optimization, in which we seek to maximise SII. The SII value was calculated with each iteration with expressions (1) and (2) considering computed sound levels. Since the objective functions and constraints are discontinuous and do not have analytic derivatives, a derivative-free Bound Optimization by Quadratic Approximation (BOBYQA) method was employed (COMSOL Multiphysics, 2015). The outcome of iterated BOBYQA is an optimized waveguide topology with a maximized SII.

For the sake of clear terminology, we distinguish between a waveguide, referring to the geometry in the computational model, and a mask insert, which is the practical (manufactured) implementation of the optimised waveguide. The optimised waveguide has an axisymmetric body shape that requires adaptation for the fabrication of a mask insert. While the waveguide elements are important from the perspective of improving speech transmission, the primary purpose of the mask insert is air filtration, necessitating the integration of elements that contain an easily cut piece of filter material. Simple square-cut shapes are easy to produce regardless of the equipment and cutting method used. Accordingly, the printed geometry has a square cross section at the filter plane, which is adapted to the circular cross section of the waveguide geometry. While we utilise a square of material cut from a disposable surgical mask, this can be replaced with any suitable filtration material. Moreover, the internal part of the mask insert should not interfere with facial expressions and be suitable for long-term wearing, which adds further constraints on the geometry of the internal mask part. The insert [Figs. 1(d) and 1(e)] was fabricated using an extrusion 3D printer (Comgrow 3D Technology Co., Shenzhen, China, https://www.creality3dofficial.com/products/official-creality-ender-3-3d-printer) using Polylactic Acid (PLA) filament, a widely available and inexpensive material for extrusion 3D printing. Important for the widespread implementation of our designs, inexpensive extrusion 3D printing is suitable for fabrication of complex shape objects.

Experimental trials were performed in order to confirm enhanced speech transmission. The experimental setup consists of a mannequin head with digital speaker, the designed respirator (mask and mask insert), a microphone and stands (Fig. S1 in the supplementary material)¹. A silicone sealant was applied to the mask edge to prevent fugitive acoustic emissions. A silicone mannequin head was used to replicate both the approximate shape of the mouth and head, and to approximate human skin since they have similar acoustic impedance characteristics (Clark et al., 2006; Zell et al., 2007). A wireless sound speaker (SP-M12, Huizhou Falili Plastic Products Co., Guangdong, China, https://www.aliexpress.com/item/10000049336587.html) was placed inside the mannequin head (in the mouth position, speaker membrane flush with the lips). An omni-directional microphone (Boya BY-M1, Shenzhen Jiayz Photo Industrial, Shenzhen, China, http://www.boya-mic.com/lavaliermicrophones/BY-M1.html) was fixed at the distance 1 m in front of the sound source. The specifications of both the speaker (100 Hz to 20 kHz) and microphone (65 Hz to 18 kHz) frequency bandwidth cover the test spectrum (250 Hz to 8 kHz). For each case, a sine wave was generated by the speaker at each of the discrete frequencies used to assess SII. The sound transmission measured by evaluating the recorded signal level. Since the recording was conducted in a quiet room (Fig. S1 in the supplementary material)¹, the acquired level was attributed purely to the emitted signal.

Our numerical results clearly demonstrate that the resuscitator mask reduces acoustic transmission compared to maskless (unencumbered) speech (see Video SuppPubmm1 in the supplementary material)¹. Figures. 3(a) and 3(b) display the numerical and experimental spectrum of the Insertion Loss (IL) compared to the (maskless) baseline, namely, the reduction in SPL at a 1 m distance due to attenuation and reflection and attenuation of sound energy within the mask. The IL values for the mask case are positive for most of the spectrum, indicating the mean speech level was reduced. Simulated SPL fields for 1, 2, 4, and 8 kHz sound excitation with and without the mask are presented on Figs. 4(a), 4(b) and 5. Figure 5 shows the SPL along the axis of symmetry (centreline of mask). The sound reflection from the internal surface of the mask partly amplifies SPL in the internal compartment (Z < 50 mm). However, the mask reduces the sound transmission overall, showing a much lower SPL level outside the mask in comparison to the reference normal voice, resulting in a simulated SII reduction from 0.691 to 0.322 displayed in Table I.

Briefly, we interpret these results to demonstrate how the mask modifies sound transmission, with wave energy being reflected from and absorbed by internal mask surfaces. An acoustic wave incident on the skin or mask surface is partly transmitted, but, due to impedance mismatch between air and other materials, more than 99% of acoustic energy is reflected. The reflectivity of mask surfaces and a small mask throat cross section enclose the acoustic energies between the mask and face, ultimately resulting in acoustic energy dissipation within mask materials and skin. The sound interference is defined by the geometry of this chamber and generally is difficult to analytically predict due to its complex shape. However, with reasonable assumptions, we can predict resonances based on the mask geometry's principal length scales. For example, the internal volume can be considered as a Helmholtz resonator with the mask throat acting as the resonator port. The resonance frequency of a Helmholtz resonator is defined by the speed of sound in air (⁠$c=343 m/s$⁠), resonator volume (⁠$V=1.4·105 mm3$⁠), the throat length (⁠$l=17.1 mm$⁠), and diameter (⁠$d=21.8 mm$⁠), and can be estimated using (Chanaud, 1994)

For the resonator (the mask geometry), the resonance frequency is 477 Hz, which corresponds to the high transmission, negative IL in Fig. 3(a). This effect is known for bandpass loudspeaker systems or subwoofers that have similar designs (Polack et al., 2001; Sirakov, 2009). Such systems have high transmission at this resonant frequency, but the response degrades for higher (and lower) bands. We observe the same effect in our system, with far lower transmission efficiency at off resonance frequencies.

With higher frequencies, especially with wavelengths on the order of the mask dimensions and smaller, further resonant effects are observed in the numerical study. For example, the mask internal space may be considered as a half-wave resonator with two closed ends. If we consider the distance between the mouth and the mask surface in front of it, the equivalent resonator is 33.4 mm long and the half-wave resonance frequency is 5.1 kHz. This frequency shows relatively good transmission through the mask. One-quarter and three-quarters wavelengths instead correspond to off resonance frequencies, 2.6 and 7.7 kHz, respectively, at which points the IL approaches local maxima. The complex shape of the IL results, however, from the non-rectilinear, non-uniform mask geometry, with the mask width and curved mask geometry also contributing to the IL curve shape. A further resonance mode can be related to the throat of the mask as well. A plane acoustic wave passing through an aperture is partly reflected due to the abrupt change of characteristic acoustic impedance. The mouth and the mask aperture, spaced 51.5 mm apart, constitute an open-end quarter-wave resonator where one-quarter and three-quarters resonance frequencies are 1.6 and 5.0 kHz. Due to the interference with other resonant modes, it is difficult to distinguish the impact of the resonator, but the system transmits the sound relatively well at the frequencies listed. Moreover, at the half-wave antiresonance frequency, 3.3 kHz, numerical simulations indicate that the mask is expected to feature high sound transmission loss.

Having elaborated on these results in terms of mask resonance modes, the simulation results nevertheless demonstrate reduced sound transmission in the bulk of the frequency range (from 0.7– 5.5. kHz), where increased IL in this range is related to reduced SII values. To quantify the speech degradation, SII values measured for these cases are summarised in Table I. To improve the transmission of acoustic energy, we implemented iterative numerical shape optimisation for acoustic waveguide elements that improves the overall system SII, where Fig. 6 shows the improvement in SII with increasing iteration count. Our numerical optimisation resulted in two distinct waveguides, with two different set dimensions sizes of the external part at 20 and 36 mm long. The optimized waveguide geometries have resulting bell-shaped acoustic horns for internal and external parts of the waveguide with flanges normal to the axis of the symmetry. Figures. 2(b) and 2(c) display a cross sectional view of the waveguides inserted into the mask. Figures. 4(c), 4(d), and 5 illustrate the sound level maps of the optimised waveguides.

The variation in frequency-dependent characteristics between the base mask (without waveguide) and modified mask geometry (with inserted waveguide) can be attributed to the different geometric elements that make up each simulated system. The IL of the waveguides attached to the mask is comparable or marginally greater at frequencies up to 1.5 kHz, with slightly narrowed throat dimensions arising from the waveguide shell thickness. The waveguides have 2 mm thick walls, reducing the cross section area of the duct by 33%, somewhat reducing the Helmholtz resonance efficiency. Moreover, the variation in dimensions within the mask geometry resulted in a Helmholtz resonance frequency reduction of 0.1 kHz, reflected on the IL curve. Another feature of note in the IL spectrum is a peak IL at 3.5 kHz, similar to the peak mask absorption at 3.7 kHz. This frequency reduction we relate to a slight increase in the quarter-wave resonator length when the waveguide is attached. In fact, the length between the mouth and the aperture is increased by the stretched and gradually expanding duct of the waveguide. Regardless of these minor resonance frequency shifts, the overall performance of the masks (with and without waveguide) is comparable at lower frequencies, owing to the physical limitations imposed by narrow throat dimensions in both cases, whereas otherwise, the waveguides serve to vastly improve overall performance, especially at frequencies higher 1.5 kHz. This is supported by the numerically evaluated SII values, which are 0.590 and 0.569 for 36  and 20 mm waveguides, respectively, showing a much higher value in comparison to the mask alone.

In order to further understand contributions of individual parts of the waveguide, we performed additional simulations where the mask was combined with each part of the 36 mm waveguide separately. Results are presented in Fig. 3(c), displaying the Insertion Gain (IG), which is the SPL level increase relative to the baseline of the mask alone. Since the external part acts primarily as an acoustic horn, it improves the sound transmission at relatively higher frequencies (i.e., >1.6 kHz) where its size is comparable with or larger than the acoustic wavelength. The internal part further enhances speech delivery at the middle range of the spectrum (1.8–5.5 kHz), which we interpret as its ability to direct acoustic reflections toward the waveguide throat. Notably, the total waveguide IG at frequencies above 2 kHz is roughly the sum of values for each of interior and exterior components, though is not the case for lower frequencies. At frequencies lower than 2 kHz, the internal waveguide parts are smaller than one-quarter of the acoustic wavelength, preventing significant modification of wavefront interactions. In total, simulations show low SII values without all waveguide components, underlining the critical contribution of both parts of the waveguide to enhancing speech intelligibility. These results are summarized in Table I.

Whereas the simulation and experimental tests in Figs. 2 and 5 serve to demonstrate the efficacy of the optimised acoustic waveguide approach for improved speech transmission, the geometry requires additions and minor modifications to create a wearable respirator. The printed inner cone features, for example, can impinge on the user's nose, necessitating an elongation along the vertical axis. Nevertheless, other sections of the internal part follow the optimised geometry. The internal and external parts of the attachment were further designed to connect to each other in the mask throat using clipping elements. The assembly requires no tools and provides a reliable connection to prevent air leakage [see Figs. 1(d), 1(e), S2, and Video SuppPubmm2 in the supplementary material)¹. The resuscitator mask alone weighs 110 g, the 36 and 20 mm inserts weight 41 and 30 g, resulting in gross weight of these assemblies of 151g and 140 g, respectively.

The external cone of the waveguide was modified so that a filter and cover component could be added. The filter material is held by a 5 mm wide perimeter contact zone between these two parts to permit variations in filter insert dimensions and ensure a good seal around the filter edges. A lattice grid was also added to support the filter material and prevent its collapse during use. Further, because rectilinear filter inserts are far easier to cut and size appropriately than circular ones, the cross section at the outer extent of the waveguide was modified into a 50 × 50 mm square. The filter cover component is attached to the waveguide via flexible clips, with filter components with thicknesses on the order of 1 mm or less being easily inserted and clamped.

Despite apparent differences between the numerical and experimental results, they share similar trends and attributes [Fig. 3(b) and 3(d)]. Since the Helmholtz resonators are generally considered unsusceptible to volume shape, but are rather defined by the volume size, we observe good data agreement for low frequencies (up to 1.6 kHz). At the higher frequencies, however, the precise resonator shape defines the sound transmission, demonstrating why resonance peaks may be somewhat misaligned in comparison with simulation findings. Notably, the resuscitation mask geometry is a complex 3D shape whose specific resonance modes may vary slightly as compared to the 2D simulation space in which the optimization was performed.

Nevertheless, waveguide-based mask inserts were shown to reduce the IL for the majority of the spectrum [Fig. 3(b)]. The experiments resulted in the SII values 0.526 and 0.497 for the 36 and 20 mm inserts, noticeably higher than the value measured for the mask alone at 0.453. The larger insert overall exhibits superior performance, but in some environments, the smaller insert may nevertheless be preferable due to its compact size.

The addition of separate 36 mm mask insert components in Fig. 3(d) highlights the dominating role the external part plays for sound transmission. Indeed, the outer attachment exhibits similar performance and frequency response to the numerical study and boosts the transmission over middle and high frequencies (1.5–8 kHz), whereas the internal part has a mild impact on the mask sound transmission. Regardless, the fully assembled mask insert provides higher overall speech transmission than any segment alone, as shown in Table I. Though a layer of filtration material cut from a surgical mask reduced the speech intelligibility marginally, the SII value is still higher than one for the baseline mask (in which no such filter is present). The directivity of the respirator was also evaluated by rotating the microphone with respect to the 36 mm respirator in the horizontal plane. The polar diagram (Fig. S3 in the supplementary material)¹ shows the stable emission level at angles <45$°$⁠, creating a substantial cone within which sound can be effectively transmitted.

The Association of Australasian Acoustical Consultants gives recommendations for ambient (background) noise levels inside healthcare facilities; the A-weighted equivalent continuous sound level for unoccupied rooms is recommended to be below $LAeq,T=35$ – $55$ dB, depending on the medical facility (Association of Australasian Acoustical Consultants, 2017). The A-weighted noise level used in our study from actual measurements, however, is $LA=59.5$ dB (Kracht et al., 2007), underlining the challenging environment in real-world hospital environments. Therefore, every improvement in SII can translate to better comprehension, where values between 0.45 and 0.5 are commonly recommended as a threshold between being able to understand complex instructions versus only being able to transmit simple messages (Pope and Miller-Klein, 2016). That the simulated and realised mask inserts yielded SII values above this threshold even in a noise environment measured above recommended levels demonstrates that the optimised designs are appropriate for a wide range of working environments, and that this optimization approach can yield marked and meaningful improvements in speech intelligibility.

Measured SII deviation from the simulation results can therefore partly be attributed to the limitations of the axisymmetric numerical study. This simulation environment utilized isotropic idealized materials that did not consider surface roughness, where attenuation of acoustic energy within these materials was not considered. The 3D printed polymer materials used may also differ in their bulk properties from the idealized, isotropic materials utilised in the simulation environment. Moreover, even though the cross sectional shape of the waveguide matches that in the simulation case, the waveguide nevertheless required small adaptations in order to be coupled to the resuscitation mask (two-piece components and fitting, potentially with small gaps) and hold a piece of filter material, all of which can impact mask performance.

The study presents a numerical optimisation procedure allowing us to improve speech intelligibility through a facemask to optimise sound transmission in the frequency bands most important to speech intelligibility. We successfully implement this approach to design a filtration insert converting a resuscitator mask into a respirator while considering speech transmission. Whereas the base resuscitator mask geometry limits the transmission of acoustic energy, our numerical optimization permits the design of an acoustic waveguide geometry that enhances sound transmission. Whereas the resuscitation mask alone results in low speech intelligibility scores in both simulation and experimental cases, the addition of the optimised waveguide elements improves this markedly. The resulting respirators, being extensions of commercial devices, are comfortable to wear for long periods, provide a tight seal, and are suitable for a range of disposable filter materials. Moreover, the entire design can readily be fabricated using inexpensive personal-grade 3D printers, making it suitable for wide use in otherwise resource-poor settings. Even though this computational design approach was implemented for an axisymmetric method, it can be further generalized for a 3D framework as well. While continuous noise sources are appropriate for the present study, in which the primary purpose is to examine the impact of geometry changes in the presence of constant background conditions, extended SII criteria can be used to account for fluctuating noises in the speech evaluation process (Rhebergen et al., 2008; Soli et al., 2018). These results have wider implications for not only other respiration systems, including commercially produced ones, but wherever acoustic transmission through constrained geometries is desired.