Water and heat exchanges in mammalian lungs.

A secondary function of the respiratory system of the mammals is, during inspiration, to heat the air to body temperature and to saturate it with water before it reaches the alveoli. Relying on a mathematical model, we propose a comprehensive analysis of this function, considering all the terrestrial mammals (spanning six orders of magnitude of the body mass, M) and focusing on the sole contribution of the lungs to this air conditioning. The results highlight significant differences between the small and the large mammals, as well as between rest and effort, regarding the spatial distribution of heat and water exchanges in the lungs, and also in terms of regime of mass transfer taking place in the lumen of the airways. Interestingly, the results show that the mammalian lungs appear to be designed just right to fully condition the air at maximal effort (and clearly over-designed at rest, except for the smallest mammals): all generations of the bronchial region of the lungs are mobilized for this purpose, with calculated values of the local evaporation rate of water from the bronchial mucosa that can be very close to the maximal ability of the serous cells to replenish this mucosa with water. For mammals with a mass above a certain threshold ([Formula: see text] kg at rest and [Formula: see text] g at maximal effort), it appears that the maximal value of this evaporation rate scales as [Formula: see text] at rest and [Formula: see text] at maximal effort and that around 40% (at rest) or 50% (at maximal effort) of the water/heat extracted from the lungs during inspiration is returned to the bronchial mucosa during expiration, independently of the mass, due to a subtle coupling between different phenomena. This last result implies that, above these thresholds, the amounts of water and heat extracted from the lungs by the ventilation scale with the mass such as the ventilation rate does (i.e. as [Formula: see text] at rest and [Formula: see text] at maximal effort). Finally, it is worth to mention that these amounts appear to remain limited, but not negligible, when compared to relevant global quantities, even at maximal effort (4-6%).

Propagation of an idealized infection in an airway tree, consequences of the inflammation on the oxygen transfer to blood.

A mathematical model of infection, inflammation and immune response in an idealized bronchial tree is developed. This work is based on a model from the literature that is extended to account for the propagation dynamics of an infection between the airways. The inflammation affects the size of the airways, the air flows distribution in the airway tree, and, consequently, the oxygen transfers to blood. We test different infections outcomes and propagation speed. In the hypotheses of our model, the inflammation can reduce notably and sometimes drastically the oxygen flow to blood. Our model predicts how the air flows and oxygen exchanges reorganize in the tree during an infection. Our results highlight the links between the localization of the infection and the amplitude of the loss of oxygen flow to blood. We show that a compensation phenomena due to the reorganization of the flow exists, but that it remains marginal unless the power produced the ventilation muscles is increased. Our model forms a first step towards a better understanding of the dynamics of bronchial infections.

Beneficial short-term effect of autogenic drainage on peripheral resistance in childhood cystic fibrosis disease.

BACKGROUND: Airway clearance techniques are supposed to be a necessary adjunct for the enhancement of impaired peripheral clearance in cystic fibrosis (CF). The objective was to assess the effect of one physiotherapy session (autogenic drainage: AD) on mucus clearance (sputum wet weight) and impulse oscillometry system (IOS) indices, including those obtained from extended Resistance-Inertance-Compliance (eRIC) modelling, considering the degree of bronchial congestion. METHODS: Thirty children with CF (median age: 12.7 years) in a stable condition prospectively underwent IOS measurements at baseline and after AD. They were divided in two groups: with (visual analog scale of bronchial congestion by the physiotherapist ≥ 5/10) and without (scale < 5/10) bronchial congestion. Paired-comparison of the effects of AD on airway resistance measurements was done with Wilcoxon test. RESULTS: The congestion scale correlated with the wet weight of sputum production during the session (Pearson test: p < 0.0001, R = 0.66). Ten children had bronchial congestion and 20 were without congestion. In the whole group, R5-20 Hz significantly decreased after AD (P = 0.049), which was related to a decrease in the children with congestion (P = 0.025), whereas it was not significantly modified in the children without congestion (P = 0.327). The eRIC model allowed the calculation of the peripheral resistance of the respiratory system, which also decreased in the children with congestion (P = 0.037), however, not modified in the children without congestion (P = 0.390). CONCLUSION: One session of autogenic drainage has the ability to decrease peripheral resistance obtained from IOS measurements, more specifically in children with CF with moderate to severe bronchial congestion. TRIAL REGISTRATION: ClinicalTrials.gov Identifier: NCT04094441.

Is airway damage during physical exercise related to airway dehydration? Inputs from a computational model.

In healthy subjects, at low minute ventilation (V̇e) during physical exercise, the water content and temperature of the airways are well regulated. However, with the increase in V̇e, the bronchial mucosa becomes dehydrated and epithelial damage occurs. Our goal was to demonstrate the correspondence between the ventilatory threshold inducing epithelial damage, measured experimentally, and the dehydration threshold, estimated numerically. In 16 healthy adults, we assessed epithelial damage before and following a 30-min continuous cycling exercise at 70% of maximal work rate, by measuring the variation pre- to postexercise of serum club cell protein (cc16/cr). Blood samples were collected at rest, just at the end of the standardized 10-min warm-up, and immediately, 30 min and 60 min postexercise. Mean V̇e during exercise was kept for analysis. Airway water and heat losses were estimated using a computational model adapted to the experimental conditions and were compared with a literature-based threshold of bronchial dehydration. Eleven participants exceeded the threshold for bronchial dehydration during exercise (group A) and five did not (group B). Compared with post warm-up, the increase in cc16/cr postexercise was significant (mean increase ± SE: 0.48 ± 0.08 ng·L-1 only in group A but not in group B (mean difference ± SE: 0.10 ± 0.04 ng·L-1). This corresponds to an increase of 101 ± 32% [range: 16%-367%] in group A (mean ± SE). Our findings suggest that the use of a computational model may be helpful to estimate an individual dehydration threshold of the airways that is associated with epithelial damage during physical exercise.NEW & NOTEWORTHY Using a computational model for heat and water transfers in the bronchi, we identified a threshold in ventilation during exercise above which airway dehydration is thought to occur. When this threshold was exceeded, epithelial damage was found. This threshold might therefore represent the ventilation upper limit during exercise in susceptible individuals. Our results might help to prevent maladaptation to chronic exercise such as exercise-induced bronchoconstriction or asthma.

Interplay Between Optimal Ventilation and Gas Transport in a Model of the Human Lung.

Ventilation is at the origin of a spending of energy coming from air circulation in the bronchial tree and from the mechanical resistance of the tissue to motion. Both amplitude and frequency of ventilation are submitted to a trade-off related to this energy, but they are also submitted to a constraint linked to the function of the lung: to transport enough oxygen and carbon dioxide in order to respect metabolism needs. We propose a model for oxygen and carbon dioxide transport in the lung that accounts for the core physical phenomena: lung's tree-like geometry, transport of gas by convection and diffusion, exchanges with blood and a sinusoidal ventilation. Then we optimize the power dissipated by the ventilation of our model relatively to ventilation amplitude and period under gas flow constraints. Our model is able to predict physiological ventilation properties and brings interesting insights on the robustness of different regimes. Hence, at rest, the power dissipated depends very little on the period near the optimal value. Whereas, at strong exercise any shift from the optimal has dramatic effect on the power. These results are fully coherent with the physiological observation and raises the question: how the control of ventilation could select for the optimal configuration? Also, interesting insights about pathologies affecting ventilation could be derived, and our model might give insights on therapeutical responses, with specific breathing strategies or for better driving mechanical ventilation.

New insights into the mechanisms controlling the bronchial mucus balance.

In this work, we aim to analyze and compare the mechanisms controlling the volume of mucus in the bronchial region of the lungs of a healthy human adult, at rest and in usual atmospheric conditions. This analysis is based on a balance equation for the mucus in an airway, completed by a computational tool aiming at characterizing the evaporation, during respiration, of the water contained in the bronchial mucus. An idealized representation of the lungs, based on Weibel's morphometric model, is used. The results indicate that the mechanisms controlling the volume of mucus in an airway depend on the localization of the airway in the bronchial region of the lungs. In the proximal generations, the volume of mucus in an airway is mainly controlled by the evaporation of the water it contains and the replenishment, with water, of the mucus layer by epithelial cells or the submucosal glands. Nevertheless, cilia beating in this part of the bronchial region remains of fundamental importance to transport the mucus and hence to eliminate dust and pathogens trapped in it. On the other hand, in the distal generations of the bronchial region, the volume of mucus in an airway is mainly controlled by the mucociliary transport and by the absorption of liquid by the epithelium. This absorption is a consequence of the mucus displacement by the cilia along generations with an interface between the epithelium and the airway surface layer of decreasing area. The numerical results obtained are in good agreement with previously published experimental data, thus validating our approach. We also briefly discuss how our results can improve the understanding and, possibly, the treatment of pulmonary diseases.

Tissue growth pressure drives early blood flow in the chicken yolk sac.

BACKGROUND: Understanding how molecular and physical cues orchestrate vascular morphogenesis is a challenge for developmental biology. Only little attention has been paid to the impact of mechanical stress caused by tissue growth on early blood distribution. Here we study the peripheral accumulation of blood in the chicken embryonic yolk sac, which precedes sinus vein formation. RESULTS: We report that blood accumulation starts before heart-induced blood circulation. We hypothesized that the driving force for the primitive blood flow is a growth-induced gradient of tissue pressure in the yolk sac mesoderm. Therefore, we studied embryos in which heart development was arrested after 2 days of incubation, and found that yolk sac growth and blood peripheral accumulation still occurred. This suggests that tissue growth is sufficient to initiate the flow and the formation of the sinus vein, whereas heart contractions are not required. We designed a simple mathematical model which makes explicit the growth-induced pressure gradient and the subsequent blood accumulation, and show that growth can indeed account for the observed blood accumulation. CONCLUSIONS: This study shows that tissue growth pressure can drive early blood flow, and suggests that the mechanical environment, beyond hemodynamics, can contribute to vascular morphogenesis. Developmental Dynamics 246:573-584, 2017. © 2017 Wiley Periodicals, Inc.

A multiscale model of placental oxygen exchange: The effect of villous tree structure on exchange efficiency.

The placenta is critical to fetal health during pregnancy as it supplies oxygen and nutrients to maintain life. It has a complex structure, and alterations to this structure across spatial scales are associated with several pregnancy complications, including intrauterine growth restriction (IUGR). The relationship between placental structure and its efficiency as an oxygen exchanger is not well understood in normal or pathological pregnancies. Here we present a computational framework that predicts oxygen transport in the placenta which accounts for blood and oxygen transport in the space around a placental functional unit (the villous tree). The model includes the well-defined branching structure of the largest villous tree branches, as well as a smoothed representation of the small terminal villi that comprise the placenta's gas exchange interfaces. The model demonstrates that oxygen exchange is sensitive to villous tree geometry, including the villous branch length and volume, which are seen to change in IUGR. This is because, to be an efficient exchanger, the architecture of the villous tree must provide a balance between maximising the surface area available for exchange, and the opposing condition of allowing sufficient maternal blood flow to penetrate into the space surrounding the tree. The model also predicts an optimum oxygen exchange when the branch angle is 24 °, as villous branches and TBs are spread out sufficiently to channel maternal blood flow deep into the placental tissue for oxygen exchange without being shunted directly into the DVs. Without concurrent change in the branch length and angles, the model predicts that the number of branching generations has a small influence on oxygen exchange. The modelling framework is presented in 2D for simplicity but is extendible to 3D or to incorporate the high-resolution imaging data that is currently evolving to better quantify placental structure.

Deformability-Based Electrokinetic Particle Separation.

Deformability is an effective property that can be used in the separation of colloidal particles and cells. In this study, a microfluidic device is proposed and tested numerically for the sorting of deformable particles of various degrees. The separation process is numerically investigated by a direct numerical simulation of the fluid⁻particle⁻electric field interactions with an arbitrary Lagrangian⁻Eulerian finite-element method. The separation performance is investigated with the shear modulus of particles, the strength of the applied electric field, and the design of the contracted microfluidic devices as the main parameters. The results show that the particles with different shear moduli take different shapes and trajectories when passing through a microchannel contraction, enabling the separation of particles based on their difference in deformability.

Toward the modeling of mucus draining from human lung: role of airways deformation on air-mucus interaction.

Chest physiotherapy is an empirical technique used to help secretions to get out of the lung whenever stagnation occurs. Although commonly used, little is known about the inner mechanisms of chest physiotherapy and controversies about its use are coming out regularly. Thus, a scientific validation of chest physiotherapy is needed to evaluate its effects on secretions. We setup a quasi-static numerical model of chest physiotherapy based on thorax and lung physiology and on their respective biophysics. We modeled the lung with an idealized deformable symmetric bifurcating tree. Bronchi and their inner fluids mechanics are assumed axisymmetric. Static data from the literature is used to build a model for the lung's mechanics. Secretions motion is the consequence of the shear constraints apply by the air flow. The input of the model is the pressure on the chest wall at each time, and the output is the bronchi geometry and air and secretions properties. In the limit of our model, we mimicked manual and mechanical chest physiotherapy techniques. We show that for secretions to move, air flow has to be high enough to overcome secretion resistance to motion. Moreover, the higher the pressure or the quicker it is applied, the higher is the air flow and thus the mobilization of secretions. However, pressures too high are efficient up to a point where airways compressions prevents air flow to increase any further. Generally, the first effects of manipulations is a decrease of the airway tree hydrodynamic resistance, thus improving ventilation even if secretions do not get out of the lungs. Also, some secretions might be pushed deeper into the lungs; this effect is stronger for high pressures and for mechanical chest physiotherapy. Finally, we propose and tested two a dimensional numbers that depend on lung properties and that allow to measure the efficiency and comfort of a manipulation.

An archetypal mechanism for branching organogenesis.

Branched structures are ubiquitous in nature, both in living and non-living systems. While the functional benefits of branching organogenesis are straightforward, the developmental mechanisms leading to the repeated branching of epithelia in surrounding mesoderm remain unclear. Both molecular and physical aspects of growth control seem to play a critical role in shape emergence and maintenance. On the molecular side, the existence of a gradient of growth-promoting ligand between epithelial tips and distal mesenchyme seems to be common to branched organs. On the physical side, the branching process seems to require a mechanism of real-time adaptation to local geometry, as suggested by the self-avoiding nature of branching events. In this paper, we investigate the outcomes of a general three-dimensional growth model, in which epithelial growth is implemented as a function of ligand income, while the mesenchyme is considered as a proliferating viscous medium. Our results suggest that the existence of a gradient of growth-promoting ligand between distal and proximal mesenchyme implies a growth instability of the epithelial sheet, resulting in spontaneous self-avoiding branching morphogenesis. While the general nature of the model prevents one from fitting the development of specific organs, it suggests that few ingredients are actually required to achieve branching organogenesis.

Homothety ratio of airway diameters and site of airway resistance in healthy and COPD subjects.

Our objective was to evaluate whether a decrease in the homothety ratio (h: diameter of child/parent bronchus, constant over generations) explains the shift in airway resistance toward periphery in chronic obstructive pulmonary disease (COPD). Using a validated computational model of fluid motion, we determined that reduced values of h (<0.76) were associated with a shift in resistance toward periphery. The calculated luminal diameters of terminal bronchioles using normal h (0.80-0.85) or reduced h (0.70-0.75) fitted well with measured micro-CT values obtained by McDonough et al. (N. Engl. J. Med., 2011; 365:1567-75) in control and COPD patients, respectively. A semi-analytic formula of resistance using tracheal dimensions and h was developed, and using experimental data (tracheal area and h from patients [Bokov et al., Respir. Physiol. Neurobiol., 2010; 173:1-10]), we verified the agreement between measured and calculated resistance (r=0.42). In conclusion, the remodeling process of COPD may reduce h and explain the shift in resistance toward lung periphery.

Branching geometry induced by lung self-regulated growth.

Branching morphogenesis is a widely spread phenomenon in nature. In organogenesis, it results from the inhomogeneous growth of the epithelial sheet, leading to its repeated branching into surrounding mesoderm. Lung morphogenesis is an emblematic example of tree-like organogenesis common to most mammals. The core signalling network is well identified, notably the Fgf10/Shh couple, required to initiate and maintain branching. In a previous study, we showed that the restriction by SHH of Fgf10 expression domain to distal mesenchyme spontaneously induces differential epithelial proliferation leading to branching. A simple Laplacian model qualitatively reproduced FGF10 dynamics in the mesenchyme and the spontaneous self-avoiding branching morphogenesis. However, early lung geometry has several striking features that remain to be addressed. In this paper, we investigate, through simulations and data analysis, if the FGF10-diffusion scenario accounts for the following aspects of lung morphology: size dispersion, asymmetry of branching events, and distal epithelium-mesothelium equilibrium. We report that they emerge spontaneously in the model, and that most of the underlying mechanisms can be understood as dynamical interactions between gradients and shape. This suggests that specific regulation may not be required for the emergence of these striking geometrical features.

Shape self-regulation in early lung morphogenesis.

The arborescent architecture of mammalian conductive airways results from the repeated branching of lung endoderm into surrounding mesoderm. Subsequent lung's striking geometrical features have long raised the question of developmental mechanisms involved in morphogenesis. Many molecular actors have been identified, and several studies demonstrated the central role of Fgf10 and Shh in growth and branching. However, the actual branching mechanism and the way branching events are organized at the organ scale to achieve a self-avoiding tree remain to be understood through a model compatible with evidenced signaling. In this paper we show that the mere diffusion of FGF10 from distal mesenchyme involves differential epithelial proliferation that spontaneously leads to branching. Modeling FGF10 diffusion from sub-mesothelial mesenchyme where Fgf10 is known to be expressed and computing epithelial and mesenchymal growth in a coupled manner, we found that the resulting laplacian dynamics precisely accounts for the patterning of FGF10-induced genes, and that it spontaneously involves differential proliferation leading to a self-avoiding and space-filling tree, through mechanisms that we detail. The tree's fine morphological features depend on the epithelial growth response to FGF10, underlain by the lung's complex regulatory network. Notably, our results suggest that no branching information has to be encoded and that no master routine is required to organize branching events at the organ scale. Despite its simplicity, this model identifies key mechanisms of lung development, from branching to organ-scale organization, and could prove relevant to the development of other branched organs relying on similar pathways.

Don'T fall off the adaptation cliff: when asymmetrical fitness selects for suboptimal traits.

The cliff-edge hypothesis introduces the counterintuitive idea that the trait value associated with the maximum of an asymmetrical fitness function is not necessarily the value that is selected for if the trait shows variability in its phenotypic expression. We develop a model of population dynamics to show that, in such a system, the evolutionary stable strategy depends on both the shape of the fitness function around its maximum and the amount of phenotypic variance. The model provides quantitative predictions of the expected trait value distribution and provides an alternative quantity that should be maximized ("genotype fitness") instead of the classical fitness function ("phenotype fitness"). We test the model's predictions on three examples: (1) litter size in guinea pigs, (2) sexual selection in damselflies, and (3) the geometry of the human lung. In all three cases, the model's predictions give a closer match to empirical data than traditional optimization theory models. Our model can be extended to most ecological situations, and the evolutionary conditions for its application are expected to be common in nature.

Toward the modeling of mucus draining from the human lung: role of the geometry of the airway tree.

Mucociliary clearance and cough are the two main natural mucus draining methods in the bronchial tree. If they are affected by a pathology, they can become insufficient or even ineffective, then therapeutic draining of mucus plays a critical role to keep mucus levels in the lungs acceptable. The manipulations of physical therapists are known to be very efficient clinically but they are mostly empirical since the biophysical mechanisms involved in these manipulations have never been studied. We develop in this work a model of mucus clearance in idealized rigid human bronchial trees and focus our study on the interaction between (1) tree geometry, (2) mucus physical properties and (3) amplitude of flow rate in the tree. The mucus is considered as a Bingham fluid (gel-like) which is moved upward in the tree thanks to its viscous interaction with air flow. Our studies point out the important roles played both by the geometry and by the physical properties of mucus (yield stress and viscosity). More particularly, the yield stress has to be overcome to make mucus flow. Air flow rate and yield stress determine the maximal possible mucus thickness in each branch of the tree at equilibrium. This forms a specific distribution of mucus in the tree whose characteristics are strongly related to the multi-scaled structure of the tree. The behavior of any mucus distribution is then dependent on this distribution. Finally, our results indicate that increasing air flow rates ought to be more efficient to drain mucus out of the bronchial tree while minimizing patient discomfort.

Electrokinetic motion of a deformable particle: dielectrophoretic effect.

Electrokinetics-induced motion and deformation of a hyperelastic particle confined in a slit microchannel has been numerically investigated for the first time with a full consideration of the fluid-particle-electric field interactions and the dielectrophoretic (DEP) effect. When the initial orientation of a cylindrical particle with respect to the applied electric field, θ(p0), is 90°, the particle tends to curl up as a "C" shape when moving from left to right. The electrokinetics-induced particle deformation is due to the joint effects of the shear force arising from the non-uniform Smoluchowski slip velocity on the particle surface and the asymmetric DEP force with respect to the center of the deformed particle arising from the spatially non-uniform electric field surrounding the particle. The electrokinetics-induced particle deformation is opposite to that of a particle moving in the same direction subjected to a pressure-driven flow. When the initial particle orientation is 0<θ(p0) <90°, a net torque arising from the DEP effect progressively rotates and aligns the particle with its longest axis parallel to the applied electric field, thus decreasing the non-uniformity of the electric field and accordingly the particle deformation. The numerical predictions are in qualitative agreement with our previous experimental observation. The results show that the DEP effect is significant and must be taken into account in the modeling of electrokinetic motion of a deformable particle in microfluidics.

Lumen areas and homothety factor influence airway resistance in COPD.

The remodelling process of COPD may affect both airway calibre and the homothety factor, which is a constant parameter describing the reduction of airway lumen (h(d): diameter of child/parent bronchus) that might be critical because its reduction would induce a frank increase in airway resistance. Airway dimensions were obtained from CT scan images of smokers with (n=22) and without COPD (n=9), and airway resistance from plethysmography. Inspiratory airway resistance correlated to lumen area of the sixth bronchial generation of right lung, while peak expiratory flow correlated to the area of the third right generation (p=0.0009, R=0.57). A significant relationship was observed between h(d) and resistance (p=0.036; R(2)=0.14). A modelling approach of central airways (5 generations) further described the latter relationship. In conclusion, a constant homothety factor can be described by CT scan analysis, which partially explains inspiratory resistance, as predicted by theoretical arguments. Airway resistance is related to lumen areas of less proximal airways than commonly admitted.

The influence of variability on the optimal shape of an airway tree branching asymmetrically.

The asymmetry of the bronchial tree has been reported on numerous occasions, and bronchi in the lung bifurcate most of the time into a major and a minor daughter. Asymmetry is most probably bound to play a role on the hydrodynamic resistance and volume occupation of the bronchial tree. Thus, in this work, we search for an optimal asymmetric airway tree crossed by Poiseuille flow that would be a good candidate to model the distal conductive part of the lung. The geometry is controlled by major and minor diameter reduction factors that depend on the generation. We show that the optimal asymmetric tree has diameter reduction factors that are adimensional from the second level of bifurcation and that they are highly dependent on the asymmetric ratio that defines the relative sizes of the major and minor branches in a bifurcation. This optimization also gives access to a cost function whose particularity is to be asymmetric around its minimum. Thus, the cliff-edge hypothesis predicts that if the system suffers variability, then the best tree is shifted from the optimal. We apply a recent theoretical model of cliff-edge in order to measure the role of variability on the determination of the best asymmetric tree. Then, we compare our results with lung data of the literature. In particular, we are able to quantify the variability needed to fit the data and to give hypothesis that could explain, at least partially, the shift found between the optimal tree and the measures in the case of asymmetric bronchial trees. Finally, our model predicts that, even if the population is adapted at best, there always exist individuals whose bronchial trees are associated with larger costs comparatively to the average and who ought to be more sensitive to geometrical remodeling.