Gravity and human respiration: biophysical limitations in mass transport and exchange in spaceflight environments

Abstract

A major requirement for humans is a breathable atmosphere for adequate respiratory CO₂/O₂ gas exchange. In microgravity, despite environmental life support systems regulating air exchange, astronauts complain about air quality, with elevated CO₂-levels resulting in detrimental health and performance effects. Using high-fidelity computational fluid dynamics, we create a model of human respiratory ventilation to show how gravity biophysically shapes and drives respiratory exchange on Earth and in microgravity. On Earth, gravity influences gas exchange through buoyancy and biothermal convection, generating a ‘human thermal body plume’ that drives airflow around the human body, and so facilitates effective gas exchange. We show that the absence of biothermal convection in microgravity reduces this airflow around the human body. This impairs gas exchange by creating an environmental breathing deadspace immediately in front of the face, leading to significant CO₂-rebreathing, with direct implications for astronaut health and countermeasures. This model was also used to estimate engineering requirements for directed external airflow equivalent to that generated by the human thermal body plume to alleviate this problem. Our model further shows that in Earth-normal 1 g, increasing ambient air temperature can also reduce efficient respiratory exchange, resulting in breathing conditions equivalent to those in microgravity, with implications for respiratory health on Earth.

Introduction

Over the course of the last five to six decades, there has been considerable work trying to understand how spaceflight (radiation and microgravity) affects living systems, with special interest in human medicine^1,2,3. Studies have shown that the spaceflight environment induces elevated CO₂-levels and regional hypoxia in the human brain², which has been linked to lower grey matter volume and changes in vestibular connectivity⁴. Spaceflight can also affect red blood cell mass through a process called ‘neocytolysis’, which selectively leads to haemolysis of young circulating red blood cells^5,6. Other spaceflight stressors, including inactivity, isolation, and confinement, can lead to physiological and pathophysiological changes such as deconditioning and metabolic changes^7,8,9,10,11. The spaceflight environment also has a pronounced impact on the gut microbiota¹², immune system¹³, cardiovascular system¹⁴, and cognitive performance^6,15,16,17. Furthermore, literature on spaceflight performance clearly indicates that spaceflight has significant effects on human respiration, including hypercapnia, hypoxia, and anaemia, which in turn have implications for astronaut health and mission success^{3,7,8,10,18,19}. Yet, despite the Environmental Control and Life Support System (ECLSS) regulating bulk air exchange, astronauts have long complained about the quality of the breathing atmosphere on the space shuttle and the International Space Station²⁰.

The spaceflight environment is unique in that, without gravity, the basic biophysical underpinnings for the aggregation and behaviour of matter change fundamentally. For individual organisms, the factors related to the fundamental forces of gravity are subject to different types of effects²¹: some affect biological organisms directly; others affect biological organisms indirectly, as the result of microgravity-altered mass transport and exchange mechanisms of the biophysical environment in which the organism is embedded (Fig. 1). Such biophysical effects were first studied on the space shuttle and Mir, in the CHROMEX series of Arabidopsis plant reproduction experiments, which examined biophysical limitations in plant growth, flowering, and seed production^22,23,24. While direct gravitational effects are typically directly observable and measurable—we can, for example, measure changes in intracranial pressure, bone mass, or plant root curvature—, this is not true for indirect effects related to mass transport and exchange, whose influence on organisms is therefore more difficult to characterize. Yet, such indirect effects have significant impact on fundamental metabolism, membrane transport, and physiological exchange, often at critical rate-limiting steps and stages of physiological function (such as respiration and photosynthesis). In microgravity, they can lead to activation of pathophysiological stress (such as mitochondrial hypoxia, respiratory redox uncoupling, and increased plant photorespiration)²¹.

Fig. 1: The importance of natural convection and diffusion in biophysical systems.

Natural convection and advection are important biophysical processes for mass transport at the global climate ecosystem, and the human built environment scales (A, where blue arrows indicate flow of cool air, red arrows signify warm air movement). In spaceflight environments, the lack of buoyancy-driven convection has to be considered (B) in engineering human habitats with forced convection (pressure-driven flow, gray arrows). Biophysical diffusion stress, based on the fundamental “Faraday” candle model (A, B inset) is outlined in panel C, describing how inhibition of thermal buoyancy indirectly induces biophysical diffusion stress at the cellular level. A, B (human thermodynamics with candle flame insets) and Movie S1 show simulations created using computational thermodynamics demonstrating how the process of biothermal convection (BTC) can drive significant flows of fluids at the human body level, driving the human thermal body plume (HTBP). The 1 g simulation (A) framed in red depicts an earth-normal environment favoring HTBP performance (see yellow arrows), which is disrupted in microgravity (B framed in blue). Note how thermal transfer from the human body is limited to conduction through the air (white outlined arrows, inset in A, B). Portions of C were originally created in BioRender by D. M. Porterfield (2026). The inset candle flame images were modified from²⁵.

To understand the biophysical fundamentals of life on Earth, we need to better understand the role of gravity and the mechanistic features of mass transfer of the larger systems in which life is embedded. The Earth is subject to inputs of mechanical, thermal, and electromagnetic photonic energy; these manifest as gravitational convection, turbulent flow, and mixing (Fig. 1). At the systems level, gravity drives the planet’s geothermal processes, climate, and weather (Fig. 1A). Mass transport can occur in both laminar and turbulent flows (high shear) which, via disruption of unstirred boundary layers, directly modulate and reduce the impact of rate-limiting molecular-diffusional transfer within the system. Gravitational convection is also important from the human health and thermoregulation perspective because of the role that climate control plays in mass transfer in built environments (Fig. 1A). At the cellular level, in the physical domain of diffusion where gravitational convection is inhibited, limits on mass transfer and boundary layer dynamics become rate-limiting (low shear)^21,25 (Fig. 1B and C). Because of the diffusional limits for O₂/CO₂ exchange²⁵, such indirect biophysical diffusion is physically analogous to abnormal candle flame morphology in microgravity²⁶ where, due to the absence of convection and unlike on Earth, diffusion shapes the flame into a sphere (Fig. 1B and C). For cellular respiration, indirect biophysical diffusion limits are significantly inhibitory, leading to cellular metabolic stress^{7,21,24,25,26,27}, microbial virulence²⁸, pharmacologic resistance²⁹, oncogene activation³⁰, apoptosis³¹, and even direct necrosis³⁰ (Fig. 1C).

Human respiration is understood primarily through alveolar diffusion and ventilation-perfusion balance⁶, neglecting the role of gravity. Our model extends this perspective by including gravity and buoyancy, and by introducing the human thermal body plume (HTBP) and stressing the role of biothermal convection (BTC) in respiratory mass transfer. By BTC, we mean thermal convection driven by metabolic heat produced by cellular respiration; by HTBP, we understand the ‘airflow plume’ that is the result of buoyancy-driven BTC around the human body. Drawing upon Faraday’s “Chemical History of a Candle” lectures²⁶, we extend the analogy between the processes of burning a candle and human respiration to the context of microgravity (Fig. 1). In 1 g, gravitational convection drives exhaled breath upwards, like a candle flame shaped into a teardrop (Fig. 1A and C). In microgravity, where gravitational convection is absent, exhaled breath disperses away from the body isotropically rather than in any particular direction, like the spherical blue candle flame observed in space (Fig. 1B and C).

Using computational fluid dynamics (CFD), we demonstrate that the microgravity environment limits BTC and leads to reduced airflow around the human body (Fig. 1A and B) which, in turn, impairs respiratory gas exchange in space. Our simulations (Figs. 1–6) show that in microgravity the HTBP is no longer capable of driving respiratory exhalate away from the human head, resulting in an environmental breathing deadspace (“CO₂ bubble”) right in front of the face and leading to significant CO₂-rebreathing. This model has direct application to solve the long-standing puzzle of why so many astronauts have historically complained (personal correspondence) about the air quality in spaceflight, despite the fact that bulk atmosphere and airflow in space habitats are strictly controlled and regulated by environmentally controlled life support systems. Our model can be used to calculate the environmental airflow required to overcome the inhibition of the HTBP and mitigate the effect of microgravity on CO₂-rebreathing. In addition, our model can be applied to understanding thermal-induced respiratory stress on Earth, by showing that it is possible to inhibit buoyancy-driven convection in 1 g, through raising the ambient air temperature to match that of the human body core (Figs. 5 and 6). Doing so results in impaired breathing conditions equivalent to those in microgravity, including reduced O₂/CO₂ exchange and increased CO₂-rebreathing.

Fig. 2: Biophysical simulation parameters for the HTBP CFD model.

Visualization of the spectral element discretization (A) of the computational domain with boundary conditions that are imposed at the walls, which include an outflow at the corner of the room. Boundary conditions imposed on the human were defined for different temperatures/locations and velocities for the mouth (B) to model exhalation/inhalation cycles (see Eq. 4). The temperature/[CO₂] of human exhalents are 37° C and 5% (by concentration). Biophysical CO₂ exchange as a function of external airflow speed (D). Biophysical simulations of respirometric efficiency of human metabolic gas exchange can account for temperature and gravity as physical factors in human respiration. Comparison of [CO₂] concentration predicted at the mouth (C) by 2D DNS, 2D RANS and 3D RANS simulations determines that no significant difference can be observed between models.

Fig. 3: The BTC-HTBP system is altered under microgravity exposure, leading to diminished CO₂ gas exchange and respiratory efficiency.

The full simulations of [CO₂] dynamics are available to view as video files (Movie S2). Under 1 g conditions (A and insert), when candle flame morphology is nominal, airflow is following the HTBP during numerous cycles and various stages (i, ii, iii, iv) of ventilatory breathing. In contrast, the microgravity environment (0 g, B) is associated with inhibition of buoyancy-driven flow, resulting in a diffusion-only environment that limits combustion and mass transport, and that physically constrains and deforms the morphology of a burning candle. (B, insert). The flow patterns of exhaled breath in microgravity resemble the morphology of the microgravity candle flame, acting like a “trapped bubble” at the source (B). The graph (C) shows the cumulative CO₂ released, normalized by the potential maximum exhaled, during a normal gravitation-exposed respiratory cycle (solid red line plot) and CO₂ release under microgravity conditions (solid blue line plot) as a result of CO₂-rebreathing in microgravity. Also shown is the tracking of the concentration of CO₂ at the mouth during the inhalation phase of the ventilatory cycle in microgravity (blue triangle, dashed plot), which is significantly higher than under 1 g conditions (red circle, dashed plot). This difference can be appreciated from the beginning of the respiratory cycle (i and ii) where these plotted profiles show that fairly low CO₂ exposure levels are favored in the 1 g environment as compared to the microgravity simulations, especially during peak levels of CO₂-rebreathing. At times the measured CO₂ concentrations are roughly equivalent (iii) but overall trends reveal both average and peak (iv) CO₂ are functionally elevated in microgravity. The plots of net exhaled CO₂ release (C) indicate that microgravity exposure (blue line plot) is associated with biophysical CO₂-rebreathing in spaceflight when compared to 1 g conditions (red line plot). The inset candle flame images were modified from²⁵.

Fig. 4: Biophysically relevant patterns of respiratory airflow and the HTBP in microgravity.

HTBP flow patterns are driven by buoyancy-driven convection and are gravity dependent, just like a candle flame (A). Time points of maximal inspiratory and expiratory velocity (B) are depicted in (C–F). Note how peak inhale/exhale patterns of velocity magnitude (C and D) and projected air velocity (E, F) change due to gravitational forces. The impact of biothermal convective airflow and the HTBP is significant in terms of limiting and restricting buoyant forces. Our results show how the HTBP perfectly barters the efficient exchange of respiratory O₂/CO₂, which is associated with mitochondrial metabolism. On Earth, being exposed to normal gravity (C and E), a prominent white-banded envelope of airflow (E) is formed at the base of the chin and directed upwards and away from the face at approximately a 45° angle. Under 1 g conditions, this white-banded envelope separates two high velocity volumes of moving air, as indicated by the dark blue and red masses (E). In contrast, in microgravity (F) the prominent white-banded envelope is missing and the projected air velocities are too low to facilitate normal respiratory exchange (D). The inset candle flame images were modified from²⁵.

Fig. 5: Biophysical CO₂ exchange as a function of buoyancy-driven convection.

Biophysical simulations of respirometric efficiency of human metabolic gas exchange can account for temperature and gravity as physical factors in human respiration. The graph (A) shows net exhaled CO₂ under constant 22 °C temperature and variable gravity (blue plot, closed circles), as well as net exhaled CO₂ under 1 g terrestrial conditions combined with variable temperatures (red plot, closed squares). The cumulative CO₂ produced and released was calculated using our biophysical BTC-HTBP approach (as laid out in Fig. 2). We also include comparative data based on our CFD simulations, related to indirect biophysical diffusion (indirect biophysical diffusion solid lines vs. RANS dashed lines; see “Methods”). All results were compared to theoretical maximal levels with no physical inefficiencies (maximum exhaled CO₂). HTBP Schlieren-type simulation images depicting varying thermal conditions (22 °C to 37 °C) at constant 1 g simulation are shown (B). Temperature profiles of the HTBP (B) and y-velocity (C) visualize the decrease in the integrity of the HTBP at gravitational minimums for BTC. The plume structure is deflected towards the face as increasing air temperatures decrease the buoyancy forces associated with the temperature gradient. The standing human profile trends warmer from the feet and legs (30–33 °C) up to maximal body surface temperatures (35–37 °C) around the head, neck and chest (see CFD/indirect biophysical diffusion in “Methods”). Based on the predictions of the model (A), combinations of low gravity and high temperatures are particularly problematic, leading to potentially catastrophic conditions in spaceflight. The clip art images of the Moon and Mars are adapted from the part of Fig. 1 that was originally designed by D.M. Porterfield (2026) using BioRender.

Fig. 6: Simulation of the HTBP under Earth-normal, microgravity, and terrestrial thermal stress conditions.

Environmental temperature and gravitational force are interchangeable in defining CO₂ accumulation (A) and projected air velocity (B). Profiles of CO₂ (A) and air velocity (B) for terrestrial gravity (1 g/22 °C), microgravity (μg/22 °C), and terrestrial hot/thermal (1 g/37 °C) conditions are shown. Notice how the breathing envelope patterns (B) observed in nominal 1 g/22 °C conditions fail when either gravity is turned off or temperature is increased. These results show that terrestrial thermal respiratory stress is equivalent to microgravity rebreathing stress in humans.

It is well-known that elevated CO₂ levels—whether in space or on Earth—have widespread detrimental effects on human physiology and performance³². Our results, therefore, have immediate implications for understanding and improving astronaut health and performance, for engineering individual biophysical countermeasures for the space environment, and for modifying and improving current ECLSS capabilities. Further, our model has the potential to unlock new doors for therapies and treatments of respiratory disease on Earth. This is important in an era in which global warming and more frequent and severe heatwaves increasingly bring about temperatures that are sufficiently high to negatively affect human respiratory exchange. On a more general level, our model demonstrates how gravity affects the fundamental biophysical mechanism of human respiration.

Results

Simulating BTC and the HTBP under 1 g and in microgravity

The fundamental biophysical mechanism of BTC creates the HTBP, which mechanistically facilitates heat/redox exchange via mass transport around the human body (Fig. 1). But to what extent does the HTBP contribute to thermal/respiratory mass transport and redox exchange? We answer this question using biophysical simulations (Figs. 1 and 2) of respiratory efficiencies of CO₂ exchange (Figs. 3 and 4), simulating CO₂ concentration distribution profiles associated with human respiratory exchange as a function of gravity, ranging from 1 g to microgravity (Figs. 5 and 6). Our approach is biocomputational: we use CFD (Fig. 2) to create a biophysical workspace to simulate BTC and the HTBP during respiration (Figs. 1 and 3). Our model is designed to accommodate the computational volume required to simulate the appropriate conditions for determining the full impact of BTC and the HTBP on human mass transport and CO₂ exchange. It was simulated in a volume of space large enough to allow for full coverage of the human body and therefore for full modelling of the HTBP (Fig. 2). It also accounts for human breathing through a novel implementation of the inflow-outflow boundary condition at the mouth. Our computational model was thus designed to accommodate all the dominant drivers of mass flow within the system.

In 1 g, under thermal conditions that favour HTBP development (room temperature 22 °C relative to body at 37 °C: ΔT=15 °C), the thermal gradient develops longitudinally on the standing human form (Fig. 3 and Supplemental Videos S1 and S2) up to the maximal flow velocities measurable at the top of the human head (0.3-0.4 m/sec). This clearly shows the gravity-dependent nature of BTC and the HTBP, and how this in turn supports respiratory gas exchange: cool dense air is warmed and buoyed upwards along the standing body surface, up into the face, and directed towards the nasal openings at the bottom of the nose protuberance. Visual validation of our simulation was achieved by comparing our 1 g results to established, previously published, redistribution patterns of heat and gasses in Schlieren imaging of human subjects³³. Under normal 1 g conditions, exhaled breath flows upwards via buoyancy, like the flame of a candle that is sculpted by the forces of gravity into a teardrop shape (Fig. 1B and C). In microgravity, exhaled breath disperses away from the human body isotropically rather than in any particular direction, like the spherical blue flame observed in spaceflight experiments²⁵ (Figs. 1–3, Movie S1 and Movie S2).

Biophysical redox exchange and gravity

The distribution of exhaled CO₂ in our simulations (Fig. 3) follows thermal gas flow patterns of mass transport and exchange associated with gravity-induced BTC (Fig. 1). Under 1 g conditions, exhaled CO₂ will simply move upwards towards the ceiling and is localized primarily in the upper 50% volume of that airspace (Fig. 3A). Under microgravity conditions, exhaled CO₂ accumulates in the lower half of the simulated volume, localized primarily at the source of emission (Fig. 3B). Since microgravity inhibits buoyancy-driven convection, the resulting “diffusion-only” environment limits combustion and mass transport, with these physical constraints leading to a deformed, spherical candle flame morphology. The pattern of flow of exhaled human breath in microgravity is also deformed, acting like a “bubble” trapped in front of its source, the human head. The model also allows us to collect relevant data regarding CO₂ concentrations at various positions and specific times throughout the simulation cycle (Fig. 3Ai-iv and Bi-iv), enabling us to precisely model and compare CO₂ release/exposure under normal 1 g (Fig. 3A) and microgravity (Fig. 3B). The mean inhalation concentration of CO₂ being rebreathed in microgravity (Fig. 3C, blue dashed line) is significantly higher than under 1 g conditions (Fig. 3C, red dashed line). This difference can be appreciated from the beginning of the respiratory cycle (Fig. 3Aii and Bii). Furthermore, due to CO₂-rebreathing, the net exhaled CO₂ in microgravity (Fig. 3C, solid blue line) is significantly lower than in 1 g (Fig. 3C, solid red line). In general, the plotted profiles show fairly low CO₂ exposure levels in the 1 g environment as compared to the microgravity simulations (Fig. 3B).

In microgravity, peak levels of CO₂-rebreathing are readily observable early in the breathing cycle (Fig. 3Civ, blue), contrasting with the later appearance of higher CO₂ levels in the 1 g control (Fig. 3Civ, red). The real-time plots of local CO₂ concentrations around the mouth calculated during our simulations (Fig. 3C) show how exhaled “CO₂ bubbles” are being rebreathed in microgravity, thereby increasing effective CO₂ exposures as compared to baseline levels expected under 1 g conditions. In 1 g, where the HTBP drives flow-induced mass transport and exchange, the transient CO₂ exposure never increases above 1.5% (Fig. 3Civ, red), whereas the microgravity simulation reveals transient CO₂ exposures above 2.5% (Fig. 3Civ, blue). Our model therefore shows that, in microgravity, indirect biophysical diffusion results in exposure to effective CO₂ levels that are approximately double those of 1 g conditions. This illustrates the impact of the indirect effects of microgravity exposure on biological systems in spaceflight.

HTBP airflow morphology

In order to fully understand how the HTBP changes, and impacts respiratory gas flow and exchange, we simulated the air pattern velocity magnitude and projected air velocities during peak inspiratory and expiratory ventilation for 1 g and microgravity (Fig. 4). On Earth, when exposed to normal gravity, a prominent pattern of HTBP-induced airflow occurs at the base of the chin and is directed upwards towards the nasal openings, and ultimately away from the face (Fig. 4C and Movie S1 and Movie S2). This airflow morphology is preserved during the changes in projected air velocity due to inhalation and exhalation, as demonstrated by the panels’ changing colour coding (Fig. 4C and E). In 1 g, the human respiratory airflow pattern is highly stable throughout the complete ventilatory cycle. In microgravity, these airflow and projection patterns are significantly different. Inhalation and exhalation airflow velocity and projection have more of a “bubble” shape, leading to CO₂ accumulation in front of the human face (Fig. 4D and F). These processes strongly mimic the thermodynamic phenomena and resulting morphology of a burning candle in 1 g and microgravity, respectively. The candle panels’ (Fig. 4A) respective arrow graphs highlight the different airflow velocities characteristic of the candle in the two environments: higher airflow velocity in 1 g due to gravitationally induced thermal convection, lower airflow velocity in microgravity due to gravitationally inhibited thermal convection. Taken together, these findings underscore the negative impact of microgravity on airflow as well as its resulting detrimental effect on human respiratory ventilation and gas exchange.

Gravitational, thermal, and redox dynamics of the HTBP

The biophysical model for human respiratory exchange is based on thermodynamics (the thermal interaction of the human body and exhaled breath, with the atmosphere driving the HTBP), overlaid with CO₂ concentration dynamics. This modelling approach is important, since it enables us to explore and compare the thermodynamic responses of the simulated human system in 1 g and in microgravity. We used our simulations to calculate cumulative physiological CO₂ release rates in response to variable gravity and changes in air temperature over a set period of breathing cycles (Fig. 5). In our 1 g simulations, the greatest levels of respiratory exchange efficiency are associated with cooler temperatures (Fig. 5). As gravity is decreased and buoyancy becomes increasingly inhibited, we see a direct correlation with decreased net CO₂ exhalation (Fig. 5A). Alternatively, we can inhibit buoyancy by raising the ambient temperature to gradually approach human body temperature (Fig. 5A red line, B and C).

As the ambient temperature increases and therefore the difference (ΔT) between the air and human body surface temperature decreases, the buoyancy driver for BTC gradually becomes suppressed. This is demonstrated in Fig. 5 A–C. At 22 °C, the plume caused by the human “thermal shell” (the conductive air layer in immediate contact with the human body) gets buoyed upwards to the head (Fig. 5B and C, leftmost panels, Movie S2). At 27 °C, the plume velocity and structural integrity decrease, but there is still enough momentum in the system for BTC transport to facilitate y-axis flow velocity for nominal CO₂ exchange (Fig. 5B and C, second panels from the left). With increasing ambient temperatures of 32 °C and 37 °C, the vertical velocity breaks down, resulting in a diminished HTBP and potential respiratory rebreathing (Fig. 5B and C, right panels). The plot (Fig. 5A) also shows that both warmer temperatures and microgravity effectively decrease respiratory gas exchange efficiencies by approximately 14% (indirect biophysical diffusion plot). Our analysis predicts that the minimal gravity threshold for Earth-normal respiratory physiological exchange is approximately 0.38 g (Fig. 5A, vertical line), which corresponds to the gravitational field strength on the surface of Mars.

Gravity and thermal rebreathing stress

To further explore the generalizability of our simulation data, we compared simulated terrestrial conditions at 22°C (Fig. 6A and B, left panels), microgravity conditions at 22 °C (Fig. 6A and B, middle panels), and terrestrial conditions with increased environmental thermal stress at 37 °C (Fig. 6A and B, right panels). 1 g conditions at 22 °C support the build-up of a respiratory breathing envelope (see labelling in Fig. 6B, left panel), ensuring optimal respiratory gas exchange in the conditions tested. In contrast, respiration in microgravity at 22 °C leads to CO₂ accumulation in front of the nasal and oral openings as a result of the collapse of this respiratory breathing envelope (Fig. 6A and B, middle panels). Lastly, when combining 1 g conditions with thermal stress of 37 °C, our data demonstrate that respiratory conditions under terrestrial heat stress are equivalent to those of microgravity, inhibiting efficient gas exchange and leading to significant CO₂-rebreathing. (Fig. 6A and B, right panels).

Discussion

Although the detrimental effects of increased CO₂ levels on human health are well-known, there is to date a paucity in modelling and simulation efforts examining the role of gravity and varying environmental temperatures in human respiratory gas exchange. Our results stress this role via highlighting the dynamics of the HTBP in microgravity as well as under terrestrial thermal stress, thereby advancing our understanding of fundamental medical biophysics in space and on Earth. Using CFD, we show how gravity and temperature biophysically shape and drive human respiratory gas exchange. We demonstrate the importance of gravitational buoyancy in mediating thermal convection in a biological system, how microgravity-induced disruption of airflow around the human body impairs respiratory O₂/CO₂ gas exchange, and visualize how this gives rise to environmental ventilation deadspaces in front of the human face—the infamous CO₂-bubbles, described by Scott Kelly²⁰ as the “bane of his existence” during his one-year mission. The fact that recent research demonstrates that declines in respiratory and aerobic capacity result in reduced human safety, diminished performance, and waning resilience during spaceflight further underscores the importance of understanding the physical properties of a breathable atmosphere in space and the ensuing biophysical consequences for human respiration. Our model further shows that increasing ambient temperatures on Earth can lead to conditions that impair human respiratory gas exchange to the same extent as the microgravity environment, a result that is especially important in the context of global warming and its associated increases in global temperature.

After underscoring and extending Faraday’s analogy between a burning candle flame and human respiration, we discuss three significant implications of our results: the consequences of our results for human pulmonary and cellular respiration in space, the significance of our results with respect to biophysical microgravity countermeasures, and the importance of our results for terrestrial human respiration in different thermal environments.

Our results reveal the interplay among biothermal convection, the HTBP, diffusion, thermal stress, and their interrelated effects on environmental mass transfer in the vicinity of the human face during respiration. Faraday²⁶, in The Chemical History of a Candle, clearly describes how cool and warm air move in order to perfectly barter the efficient exchange of combustive oxygen with CO₂ as a gravity-mediated process, even introducing the analogy between a burning candle flame and human respiration. What Faraday did not do, however, was to consider the specialized conditions of spaceflight and microgravity. Considering these conditions allows for an explanation of the similarities between the airflow patterns around a candle flame—driven by an oxidizing wax vapor plume—and the airflow patterns around the human body—driven by the human thermal body plume. Under normal Earth conditions, thermal/biothermal convection drives both plumes, resulting in efficient O₂/CO₂ exchange. Under microgravity conditions, the absence of thermal/biothermal convection and the resulting diffusion-only environment impairs efficient gas exchange. The candle flame (Figs. 1 and 3) is a perfect model in this context: like the human body, it is an example of autoconvection, a “thermally self-generating” convective system in which the thermal driver for convective mass transport—the heat of combustion—inheres in the system itself. The “heat of combustion” for biothermal convection around the human body is cellular respiration. Like a “chimney turned inside out”, metabolic heat drives airflow around the human body. The resulting HTBP performs just like the candle flame plume in directing airflow for efficient redox exchange via atmospheric gases (Figs. 1, 3, 4 and 5).

The detrimental effects of increased CO₂ inhalation on human physiology and behaviour are well-established³⁴. It is also well-known that the space environment exhibits high levels of CO₂, with ISS-ambient CO₂ ranging up to approximately 4000 ppm, which is ten times higher than Earth-ambient CO₂^32,35. Our results add to these well-known facts a novel phenomenon: they describe and explain a microgravity-induced, localized environmental deadspace immediately in front of the human face, resulting from the altered biophysical relationship between gravity and human breathing. Unlike known effects of microgravity on respiratory gas exchange, this new biophysical phenomenon is due not to the global atmospheric environment prevalent in space habitats, but to the fact that—in the absence of buoyancy-driven convection—the HTBP can no longer drive respiratory exhalate away from the human face, thereby inhibiting effective gas exchange. The resulting “CO₂ bubble” in front of the human head leads to significant CO₂-rebreathing (Figs. 3 and 4) on top of the existing high CO₂ environment, exacerbating an already detrimental problem.

Elevated CO₂, even at relatively low levels of 1000 ppm, can have pronounced biological effects. CO₂ is not inert in redox biology and directly modulates peroxide signalling and alters oxidation reactions. In addition, CO₂ accelerates ROS production, redox signalling and subsequent oxidative stress³⁶. As a modulator of cellular redox biology, CO₂ also controls the expression of genes linked to redox and NO metabolism, thereby influencing oxidative and inflammatory processes³⁷. Finally, there is mounting evidence demonstrating that CO₂ can disrupt redox homeostasis and associated oxidative stress signalling to promote accelerated bone demineralization, kidney calcification, and endothelial dysfunction^32,36,37,38.

While CO₂ alone already has detrimental effects on human performance and cellular function, we speculate that the accumulation of CO₂ in front of the face due to the disruption of biothermal convection will have synergistic pathological consequences with the effects of space radiation exposure. Radiation effects on humans are best understood from the therapeutic use of radiation therapy in cancer treatment, which causes the production of ROS, which directly contributes to radiation-induced DNA and cell membrane damage, apoptosis, necrosis, autophagy, ferroptosis, and altered immune responses^{39,40,41,42,43}. Combining increased CO₂ levels due to environmental deadspace exposure with the already existing high CO₂ levels in the space environment and space radiation effects would be expected to synergistically boost such detrimental effects in space crews. Since ROS are also produced in mitochondria by direct radiolysis of water molecules, it will be important to understand radiation-induced mitochondrial redox stress as a function of operationally relevant CO₂ levels predicted by the model. Our biophysical model of convective airflow disruption and environmental deadspace respiration suggests testable hypotheses for understanding how damaged mitochondrial respiration and impaired redox homeostasis underlie the environmental stress of space. The model also has the potential to advance our understanding of the mechanisms of human aging in space, which are known to be intimately linked to respiration and mitochondrial function^44,45.

Our results and their underlying biophysics-focused conceptual approach also have important implications for atmospheric monitoring and countermeasures during spaceflight. Existing and emerging ECLSSs – such as CDRA, Vozdukh, TAS, and CAMRAS—are bulk systems approaches for CO₂-removal from the bulk atmosphere in order to maintain an appropriate physiological atmospheric balance and CO₂ set point⁴⁶. But, even if successful in their intended application, these existing global bulk ECLSSs fail to address the localized elevated CO₂ environmental deadspace immediately in front of the human face. This means that even in a microgravity environment in which there is a properly regulated atmospheric O₂/CO₂ balance, respiration will be significantly impaired.

This situation is exacerbated for two reasons: First, the ISS is very volume-restricted. It has a total reported pressurized volume of 1005m³, of which the habitable volume is approximately 388 m³, with an air flow rate of 420–460 m³/h resulting in an air exchange rate (AER) of 1.5-2. The ISS ECLSS includes various subsystems for temperature, humidity, and atmospheric revitalization, which are operationally connected across the U.S./international and Russian segments. Second, many daily astronaut activities require stabilization and restraint through foot bars or loops, handrails, and Velcro straps; otherwise, due to the microgravity environment astronauts would float or propel themselves away from surfaces or equipment they are operating. For example, monitoring and operating the ISS’s robotic arms, performing ISS repairs, upgrades, or maintenance, such as work on electrical, life support, or data systems, all require astronauts being relatively stationary in front of control panels or behind access hatches. Astronauts are also often in a fixed position while working on the ISS’s modular equipment racks, rectangular containers that make up a significant portion of the ISS’s interior and that hold various systems, scientific experiments, and equipment necessary for the station’s life support, power, communication, and other functions. Of special note here are the Microgravity Science Glovebox (MSG) and the Life Sciences Glovebox (LSG), used for experiments involving biological samples or hazardous materials in a controlled environment, while keeping its surroundings uncontaminated. During glovebox sessions, often lasting several hours, astronauts hook their feet into restraints while also having their arms inside the built-in gloves, breathing against the glovebox surface, resulting in very little room for movement. Astronauts are also relatively stationary during exercise, taking up 1–2 h of a typical astronaut day. Both the T2 treadmill and the cycle ergometer require stabilization through harnesses or foot restraints, meaning that, even during full-body workouts, astronauts’ heads barely move. Crew further have to stabilize themselves for meals, hooking their feet under bars, with as many as six astronauts around a table at the same time—breathing at each other—, during dinner for as long as ninety minutes. Movement is also highly restricted in crew quarters, which, with a total interior volume of 2.1m^{3 47,48}, are roughly the size of a British K6 phone box⁴⁹. During sleep, 7–8 h of a typical astronaut day, astronauts zip themselves into sleeping bags or anchor themselves to a wall by fastening to one of the quarters’ walls, with only one or two inches of movement and with the head staying in more or less the same position. If there is not an available Crew Quarter, then the crewmember will anchor to a segment or use a sleeping bag anchored to a module wall and still be relatively immobile. Crew quarters are also used for other tasks (computer time, including email, video calls, writing reports, etc.), just like during sleep often with the door closed, that thus exhibit similar problems. Adding up all of these activities therefore means that astronauts are stationary for prolonged periods of time throughout their day.

Our biophysical model clearly shows and explains how microgravity exposure causes accumulation of respired CO₂ at the source of production and underscores the need for new countermeasures capable of eliminating the resulting personal environmental deadspace. One immediate such countermeasure would be to simply increase atmospheric advection to crew locations by controlling an “AI/ML smart air exchanger” as part of the vehicle’s ECLSS. As part of a more comprehensive remediation measure, our model is also currently serving as the foundation for engineering a personalized biosensor-based medical/environmental monitoring technology for controlling air exchange systems for spacecraft and space habitation systems. The need for such functional countermeasures addressing long-term requirements for future advanced deep space exploration is all the more urgent as we again advance out beyond LEO after a 50+ year hiatus. Employing a biophysical conceptual framework is essential to advancing and leveraging future capabilities and to engineering a next generation bioastronautics exploration architecture capable of supporting deep space habitation. Our model is a first component of this approach.

Our results and approach also have implications for understanding efficient respiratory gas exchange on Earth, especially as global warming and climate change pose growing threats. The effects of heat stress on individuals are well-known and include excess mortality⁵⁰, increased deaths from cardiorespiratory and other diseases, mental health issues, adverse pregnancy and birth outcomes, and increased health-care costs (reviewed in⁵¹). Extant explanations of heat stress tend to focus either on the relationship between elevated temperatures and the resulting diminished capacity of the body to thermoregulate, including its subsequent effects on the cardiovascular system, or else on respiratory effects in conjunction with air pollution and heat overload⁵². Our results add a new dimension to understanding respiratory heat stress, by underscoring the role and impact of increased temperatures on the efficiency of respiratory gas exchange via their effects on the HTBP’s ability to drive convective airflow around the human body and thus regulate human gas exchange. Convective airflow at 22 °C is optimal for the conditions tested, driving respiratory exhalate away from the face (Figs. 4, 5B and C). At 27 °C, airflow begins to be diminished (Fig. 5B and C), with noticeable impairment at 32 °C, and culminating at 37 °C when there is no difference between ambient and body core temperatures, in an environmental deadspace in front of the face (Fig. 5 B), analogous to that in microgravity (Fig. 6A and B). Thus, at 37 °C, just like in microgravity, there will be significant CO₂-rebreathing, with detrimental consequences for human respiration, cellular respiration, and metabolism.

Heat stress is already a major public health problem⁵³, with high temperatures being linked to increased emergency room visits and hospital admittance^53,54,55. This is true especially for vulnerable individuals and populations, such as the elderly, infants and young children, outdoor workers, individuals with cardiovascular disease, homeless individuals, and low-income communities (reviewed in⁵¹). Other especially vulnerable groups are those with chronic respiratory diseases, such as chronic obstructive pulmonary disease, asthma, pneumoconiosis, interstitial lung disease, or pulmonary sarcoidosis⁵⁶. This group has been undergoing rapid expansion, with the prevalence of chronic respiratory diseases increasing by 39.8% from 1990 to 2019 and, in 2019, constituting the third leading cause of death globally⁵⁷. Moreover, chronic respiratory diseases disproportionately affect low and low-middle sociodemographic index countries⁵⁷, which are also those countries particularly likely to be affected by rising temperatures in the coming decades⁵⁸. Various regions in Asia already average an ambient air temperature of 37°C during their hottest months, with several dozen cities and regions in Asia, Africa, and North and Central America not being far behind, with their hottest temperatures averaging in the low to mid-30s. Thus, these regions, if current climate model predictions are borne out, could soon manifest environmental conditions that would impair human respiratory exchange as much as the microgravity environment. Moreover, global warming has resulted in an increase in the frequency, duration, and intensity of heatwaves across the globe since the 1950s, and heatwaves with temperatures exceeding 37 °C are no longer rare occurrences^59,60.

It is thus hard to overstate the importance of adequate public health measures to address respiratory heat stress. But, doing so requires a comprehensive understanding of its various contributors. Our model identifies a novel, distinctly biophysical such factor by drawing attention to the temperature-dependence of the HTBP’s ability to regulate airflow for efficient respiratory gas exchange. It also thereby highlights the importance of truly integrated biophysical approaches for advancing our understanding of how biological organisms are embedded in their physical environments and how these environments are ‘embedded’ in them.

Drawing on advanced CFD, we adopted a modern biophysical approach to describe the inherently biophysical systems of BTC and the HTBP. The resulting model, based on biophysical thermodynamics of the human form, allowed us to demonstrate how the gravity-dependent HTBP drives human gas exchange. Our study reveals how gravity indirectly impacts living systems in spaceflight by altering the biophysical activity and bioavailability of fluids and gases required for normal physiology, leading to significant CO₂-rebreathing, despite environmental bulk atmosphere regulation. These biophysical principles scale from cells to organisms and provide the theoretical framework needed for advanced biophysical approaches to enable deep space human habitation: it is critical for future mission success to understand, embrace, and advance biophysical concepts and countermeasures as part of an integrated and comprehensive bioastronautics approach to space exploration. Our model also demonstrates how terrestrial heat stress can induce respiratory CO₂-rebreathing similar to that experienced in microgravity. Due to climate change, prolonged heat waves are becoming more common; workers exposed to this changing environment and individuals with pre-existing conditions are becoming increasingly predisposed to respiratory stress. Understanding the environmental biophysics of gravity in human health, including the role of the HTBP, thus also represents a step forward in our fundamental understanding of medical biophysics.

Methods

Governing equations

To simulate how the HTBP affects respiratory CO₂ exchange, we developed a CFD model that accounts for the main biophysical drivers of flow⁶¹. In the modelled system the two main drivers of flow are, first, the biothermal convective plume generated due to the difference in temperature between the human body and the ambient air and, second, the mechanical pulmonary respiratory flow generated during the exhalation/inhalation process of breathing. Based on the expected range of temperature, gas concentrations and velocities in the system, flow was modelled under Boussinesq approximation⁶². The range of temperature encountered in the system is between the ambient/room temperature (${T}_{\infty }=22C$^o) and nominal human body temperature (${ \sim T}_{o}=37C$^o). In this range, the effect of temperature on density of air can be assumed to be linear⁶³. To model dispersion of CO₂ during the breathing cycle, transport of CO₂ is modelled as a passive scalar. The CO₂ concentration (in air) range pertinent for the current problem does not have a significant effect on the density of air. Flow of air is modelled using the incompressible Navier-Stokes equation, with heat (temperature) and CO₂ transport modelled using two advection-diffusion equations. The non-dimensional governing equations are:

$$\frac{\partial {u}_{i}}{\partial {x}_{i}}=0;\,\frac{\partial {u}_{i}}{\partial t}+{u}_{j}\frac{\partial {u}_{i}}{\partial {x}_{j}}=-\frac{\partial P}{\partial {x}_{i}}+\frac{1}{{Re}}\frac{{{\partial }^{2}u}_{i}}{\partial {x}_{j}\partial {x}_{j}}+\theta {g}_{2;}$$

(1)

$$\frac{\partial \theta }{\partial t}+{u}_{i}\frac{\partial \theta }{\partial {x}_{i}}=\frac{1}{{Re\; Pr}}\frac{{\partial }^{2}\theta }{\partial {x}_{i}\partial {x}_{i}}$$

(2)

$$\frac{\partial \alpha }{\partial t}+{u}_{i}\frac{\partial \alpha }{\partial {x}_{i}}=\frac{1}{{Re\; Sc}}\frac{{\partial }^{2}\alpha }{\partial {x}_{i}\partial {x}_{i}}$$

(3)

The equations are made non-dimensional using the characteristic length scale (as ${L}_{c}=\frac{1}{6}m$) corresponding to the average width of a human head (see Fig. 2). Re in Eq. (1) represents the Reynolds number of the flow and is defined as $\mathrm{Re}={V}_{c}{L}_{c}/\nu$. The characteristic velocity ${V}_{c}$ is defined as ${V}_{c}=\sqrt{{g}_{c}{L}_{c}}=0.2816\,m/s$, and g_c is the characteristic acceleration scale and is calculated using the relationship ${g}_{c}=\frac{\left|{\rho }_{o}-{\rho }_{\infty }\right|}{{\rho }_{\infty }}g$. ${\rho }_{o}$ is the minimum density of air in the system that is at temperature ${T}_{o}=37C$, ${\rho }_{\infty }$ is the maximum density of air in the system that is at ${T}_{\infty }=22C$, and g is acceleration due to gravity. Kinematic viscosity of air is assumed to be $\left(\nu =1.52\times {10}^{-5}{m}^{2}{s}^{-1}\right)$, resulting in $\mathrm{Re}=3087.71\approx 3100$ for the current simulations. ${g}_{2}$ is the unit vector in the direction of acceleration due to gravity. $\theta =\frac{T-{T}_{\infty }}{{T}_{o}-{T}_{\infty }}$ is the temperature difference with respect to the ambient made non-dimensional using the reference temperature range $({T}_{{ref}}={T}_{o}-{T}_{\infty })$ of the system. The reference temperature range is kept constant for the current study, even when the ambient/room temperature (${T}_{\infty }$) has been varied. Thus, ${g}_{{eff}}=\theta {g}_{2}$ is effective gravity, which can range from 0 to 1, either through change in acceleration due to gravity (g) or variation in ambient/room temperature. In the same vein, $\alpha =\frac{C-{C}_{\infty }}{{C}_{o}-{C}_{\infty }}$ is the CO₂ concentration difference with respect to ambient CO₂ concentration ${C}_{\infty }=0.04 \%$ (~ 400 ppm), made non-dimensional using the reference CO₂ concentration range in the system (${C}_{o}-{C}_{\infty }$). ${C}_{o}=5.0 \%$ (50,000 ppm) is the concentration of CO₂ in exhaled breath⁶⁴. Pr and Sc are the Prandtl number and Schmidt number for diffusion of heat and CO₂ in air, respectively. Both have been assumed to be equal to 1 in the current model.

Boundary conditions, numerical discretization

HTBP/CO₂ exchange is simulated within a 2D domain, with the two walls and ceilings at a distance equal to the height of the standing human (see Fig. 2 A and B), so that they do not influence the dynamics of the HTBP and respiratory plume. The governing equations are solved with the initial condition of zero flow velocity in the domain, and $\theta =\alpha =0$. No-slip (Dirichlet) boundary condition is imposed for velocity and insulation (Neumann) boundary condition is applied for temperature at the walls of the room. The room has an outflow (Neumann) boundary at the lower corner to account for the flow induced by the exhalation/inhalation cycle. The human body is imposed as a no-slip boundary for velocity, with different constant temperature for different parts of the body (Fig. 2B). At the mouth, a time varying Dirichlet boundary condition is imposed for velocity of the exhalation/inhalation cycles (Fig. 2C). The breathing cycles^65,66,67 have a period of 4.00047 s: the longer exhalation cycle of 3.0115 s and a shorter (and intense) inhalation cycle of 0.98897 s. Published volumetric flow measurements from breathing experiments were utilized to develop the following equations:

$$V\left(t\right)=0.60033\sin \sin \left(0.9292t+0.4\right)\,{for}\,0 < t < 3.0115s$$

(4)

$$\begin{array}{l}V\left(t\right)=24.167{t}^{4}-338.33{t}^{3}+1777.4{t}^{2}\\\qquad\quad-\,4152.7t\,3638.99566\,\;{for}\;\,3.0115\,<\,t\,<\,4.00047\,{s}\end{array}$$

(5)

A novel implementation of the Dirichlet boundary condition was used for temperature and CO₂ fields to model the respiration dynamics accurately. During the exhalation cycle the temperature and CO₂ have the constant values of ${T}_{o}=37C$ and ${C}_{o}=5.0 \% ,$ respectively. During the inhalation cycle, the boundary condition at the mouth is imposed by taking the average temperature and [CO₂] values across multiple points in front of the mouth. This is an approximate way of imposing the Neumann boundary-condition for temperature and [CO₂] at the mouth, without switching boundary conditions during simulation. Additional simulations were conducted to study the effect of airflow through vents, on CO₂-rebreathing in microgravity, like those present at the ISS (Fig. 1B). This required modification of the computational domain to include inflow and outflow vents at the top and bottom corners, respectively. To maintain numerical stability, the outflow vents were implemented as time varying Dirichlet boundaries.

The computational domain is discretized using high-order spectral element method (SEM), with the velocity-pressure system in the incompressible Navier-Stokes equation being decoupled using the PN-PN-2 algorithm⁶⁸. The model has been implemented within the open-source high-order incompressible Navier-Stokes solver Nek5000^69,70. We used 11236 quadrilateral elements to discretize the domain with each element being further discretized using 9^th order Lagrange polynomials (N = 9), resulting in total of about 1 million nodal-points in the computational grid. Grid convergence of the results was conducted by running simulations at higher polynomial orders, and checking the difference in cumulative CO₂ released between the cases. Temporal discretization is implemented using the 3rd order semi-implicit, Backward Differencing–Extrapolation (BDF-EXT), time stepping scheme⁷¹. Nek5000 has been extensively used to solve turbulent buoyancy driven flow and heat-transfer problems^63,72 in different domains. Thus, we expect the converged simulation results to be accurate and precise. Each simulation is initialized by first running without the breathing cycle to allow the HTBP to develop. The simulations with crossflow in microgravity were initially run long enough for the background flow to reach a steady state before the breathing cycle was turned on. The velocity and structure of the simulated HTBP are qualitatively similar to published experiments^73,74 and CFD simulation^75,76,77. After the initial transient, the breathing cycle simulations were conducted for about 275 seconds of human time, which required a total of about 5000 CPU hours on AMD Rome nodes (64 cpus and 256 GB RAM) on the Notchpeak cluster at Utah CHPC.

Model comparison and limitation

The computational model was designed to account for all the dominant biophysical drivers of HTBP/CO₂ dynamics related to gravity dependent rebreathing. The goal was to resolve all the relevant physics while minimizing computational overhead. Direct numerical simulations (DNS) in 3D are possible but would require abhorrently high computational cost per simulation. Given our hypothetical model integrating gravitational mass transport with human biophysics and mechanical ventilation required about 30 simulations, including simulations conducted for grid-convergence and establishing uncertainty bounds. To check the veracity of the 2D DNS, additional simulations were conducted using 2D and 3D Reynolds Averaged Navier-Stokes (RANS) based CFD (Fig. 2C). These results support the use of 2D DNS for the current study as 3D simulations do not significantly impact the biophysical estimates of CO₂-rebreathing in microgravity, which is primarily driven by the HTBP. Microgravity results for net CO₂ exhaled from the 2D DNS and 2D RANS⁷⁸ show the same trend qualitatively between the different models (Fig. 2C). The concentrations of CO₂ observed at a virtual sensor at the mouth of the human for the different models do not show significant difference.

Additionally, two minor approximations were used in the model, which are not expected to change the general findings of this study. First, the physiological respiratory pause between inspiration and expiration was omitted to improve temporal domain processing performance. This restricted the physical model such that the impacts of physiological breathing responses would not interfere with the fundamental biophysical system analysis integrity. Second, we decided to focus on mouth breathing to avoid mixed systems models involving mixed vector flow and nasal dispersal. Both changes in breathing cycle dynamics would preferentially increase dispersal of CO₂ exhaled in microgravity over 1 g and therefore are supportive of the model and the conclusions we draw from its results.

Methods for date processing and analysis

The time varying velocity, temperature, and CO₂ fields were queried at locations of interest using virtual probes, e.g., the CO₂ concentration at the mouth during the inhalation cycle (Figs. 3, 5). To account for the fact that higher flux of CO₂ is inhaled when the inhalation velocity magnitude (v) is higher, the effective concentration of CO₂ inhaled during a cycle is calculated using Eq. 6. The cumulative volume of CO₂ exhaled is calculated using Eq. 7. Each cycle is queried at N discrete points in time during the period of interest. The period of interest could be the inhalation cycle (t_m) or across the whole simulation (t_o − t_final).

$${c}_{m}=\frac{{\int }_{{t}_{m}}v\,\cdot\,c{dt}}{{\int }_{{t}_{m}}v{dt}}=\frac{{\sum }_{1}^{N}{v}_{i}{c}_{i}}{{\sum }_{1}^{N}{v}_{i}}$$

(6)

$${V}_{{CO}2}={\int }_{{to}}^{{t}_{{final}}}{v}\,\cdot\,c{dt}=\mathop{\sum}\limits_{i}^{N}{v}_{i}{c}_{i}$$

(7)

A concept that is essential to the paper is the breathing-envelope, (Figs. 4 and 6), which is defined as the region around the human/HTBP that directs rebreathing/CO₂ flux during the inspiration-expiration cycles. A bigger breathing-envelope corresponds to lower CO₂ concentration in the inspired air. To visualize the breathing-envelope, projected velocity (v_projected(x, t)) was calculated using Eq. 8. If the velocity of air at any position x in the domain and at any given time t is given as v(x, t), and the position of the mouth of the human is specified as x_mouth. We can define a projected air velocity (v_projected(x, t)) field as follows:

$${v}_{projected}(x,t)=v(x,t)\cdot {\hat{r}}_{mouth}=v(x,t)\cdot \frac{{x}_{mouth}-x}{[{x}_{mouth}-x]}$$

(8)

v_projected (x, t) is a scalar field that is obtained by projecting air velocity at any point in the domain along a unit vector pointing in the direction of the human’s mouth from that point. This scalar field is positive for air moving towards the mouth (inspiration), and negative for air moving away from the mouth (expiration). Its magnitude represents the speed with which the air is approaching towards or moving away from the mouth.