PRESENTATION OF THE RESULTS OF NUMERICAL MODELLING OF THE EMISSION AND TRANSPORT OF AEROSOLS DURING BREATHING WITH OR WITHOUT MASK

PRESENTATION OF THE RESULTS OF NUMERICAL MODELLING OF THE EMISSION AND TRANSPORT OF AEROSOLS DURING BREATHING WITH OR WITHOUT MASK

GILLES BOUCHET

CNRS RESEARCHER, IUSTI LABORATORY – CNRS / AIX-MARSEILLE UNIVERSITY

For several years, we have been working on the development of a Virtual Nose with the ENT and Cervico-Facial Surgery Department of the AP-HM Conception Hospital. The objective of this project is to develop a multi-physical digital model of the nose to help the ENT doctor during his diagnosis, then during his dialogue with the patient, to help the ENT surgeon during the preparation of his surgical procedure by proposing the most optimal solutions, to help in the elaboration or improvement of the topical administration of drugs Since the arrival of the Coronavirus pandemic (and to prepare for future ones), we are also striving to better understand the diffusion of airborne pathogens within the nasal cavity, to better understand the penetration of pathogens through the muco-ciliary carpet and the nasal mucosa, but also their airborne transmission to the lungs, and to better understand the beneficial effects or not of nose washes and local sprays.

The objective of the work carried out in collaboration with BioSerenity, the IUSTI laboratory in Marseille, the Speech and Language Laboratory in Aix-en-Provence and the AP-HM, is to study the transmission of a virus by the respiratory route and the protection that can be provided by wearing a mask when breathing, speaking (quiet to loud voice) or singing.

Our work consists of numerically modelling breathing through the nose or mouth in humans. This involves numerically solving the equations of fluid mechanics (Navier-Stokes equations, heat equations, etc.), the same as those used to study the flow around an aircraft or in a cooling system. In our case, the flow is generated at the bottom of the oral cavity or at the bottom of the nasal cavity, the geometry used being derived either from scans performed on individuals (during medical examinations), or from dummy heads derived from the AFNOR ISO 16900-5 standard (which scans all the head shapes that can be found on Earth).

It is known that the virus is transmitted by the small droplets emitted when breathing or speaking. The transmission is modelled by solving the equations that govern the transport of particles by a flow. This phenomenon (which is still the subject of a great deal of research as there are so many applications) is quite complex as the trajectory of a particle depends on its size (which can vary over time), its density, its shape, the carrier flow, but also interactions with particles in its vicinity and the presence of solid walls….

We modelled the emission and transport of particles ranging in size from 0.1 to 100 micrometres (which allows us to scan all the particles emitted, whether in the lungs, at the level of the vocal cords or through the mouth walls (the famous sputters)). The results showed that, while large particles (above 20 micrometres) fell rapidly to the ground (ballistic trajectories) over a distance of 20 to 30 centimetres, the same was not true for smaller particles (often referred to as aerosols). Indeed, simulations showed that weakly inertial particles with a diameter of less than 5 micrometres could propagate over distances of the order of 1.5 to 2 metres in the absence of any external flow. However, these particles have a viral load that may be sufficient to transmit the virus. The initially recommended distance of 1 metre was therefore unfortunately not sufficient. Worse still, in the presence of an air current (which can be caused indoors by thermal effects, poor ventilation, the movement or breathing of multiple individuals), the sedimentation speed of these small particles is so low (of the order of 1 mm per second) that they can remain in suspension for several hours and be transported over several metres. Hence the importance of ventilating rooms well…

But the most effective protection seems to be to wear a mask. These, whether surgical or FFP2, easily stop ‘large’ particles with a diameter greater than 5 or 10 micrometres, and FFP2s also stop very small particles down to sub-micrometre diameters. Provided that they are changed regularly (when they are humidified by exhaled air, their effectiveness deteriorates) and that they are well put in place. Indeed, if they are badly positioned, there is a more or less large gap between the face and the mask, through which air passes without being filtered.

The second objective was therefore to model breathing in the presence of a mask, on the one hand to estimate the airflow rate and on the other hand to determine whether the mask is properly fitted.

A study was carried out by BioSerenity to assess the pressure drop through the mask (the fabric is a porous material that allows air to pass through the small gaps between the fibres; Like a crowd trying to squeeze through a narrow corridor, a small number of air molecules manage to pass through the gaps at the same time, causing a pressure drop; to model the presence of the mask, it is therefore sufficient to impose a local pressure drop on the mask walls). BioSerenity provided the value of this pressure drop for different air flows and different fabrics used in their masks (surgical or FFP2).

The next step was to determine the shape of the mask, which is no easy task. Indeed, the mask is made up of layers of more or less flexible fabrics, deformed by the tension on the elastics (which are put behind the ears), the deformation of a small metal piece above the nose and, of course, by the shape of the face. This work was carried out by BioSerenity using software normally used in the garment industry (it calculates the mechanical stresses inside the mask and deforms it accordingly).

The final shape of the mask will depend on the shape of the face, the tension on the elastics, the deformation of the small metal tab and the way the person positions the mask (rather on the nose, rather on the chin…). In order to cover the whole range of possibilities, it was decided to select the 5 heads from the AFNOR standard (which guarantees to cover all possible morphologies), and for each head, to deform the metal tab in three different ways (loose, medium, tight), for a surgical mask and for a FFP2 mask.

The results showed that over a breathing cycle, the leakage rate of an FFP2 mask was of the order of 6% (on a volume of exhaled air of 600 ml, 6% (i.e. 36 ml) passes over the edges of the mask, without being filtered), whereas it is of the order of 28% (i.e. 168 ml) for a surgical mask. On the bright side, an FFP2 mask filters 94% of exhaled air while a surgical mask filters 72%. The same study shows that an FFP2 mask filters 98% of inspired air while a surgical mask filters 90%.

But what is in the air exhaled through these leaks? Because of the flow during exhalation, and the greater or lesser inertia of the particles emitted (inertia which depends on their diameter), a very large proportion of the particles emitted is stopped by the mask. It can even be said that, in the case of an FFP2 mask, all particles with a diameter greater than 20 micrometres are stopped. On the other hand, a small proportion of the particles with a diameter of less than 20 micrometres manage to escape through the leakages and are suspended in the ambient air. As the diameter of these particles is very small, their fall (sedimentation) speed is very low (of the order of a millimetre per second) and the slightest flow allows them to remain in the air indefinitely.

We tested the effectiveness of wearing a mask during an ENT examination by endoscopy. We modelled the very critical situation of a doctor without a mask auscultating a patient without a mask, the critical situation of a doctor equipped with a surgical mask, then a FFP2 mask, auscultating a patient without a mask, and finally, the safe situation of a doctor equipped with a CIDALTEX® FFP Medical mask auscultating a patient equipped with a CIDALTEX® FFP-Endo mask. This last configuration ensures optimal protection.

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