The Electronic Disorder Landscape of Mixed Halide Perovskites

Band gap tunability of lead mixed halide perovskites makes them promising candidates for various applications in optoelectronics. Here we use the localization landscape theory to reveal that the static disorder due to iodide:bromide compositional alloying contributes at most 3 meV to the Urbach energy. Our modeling reveals that the reason for this small contribution is due to the small effective masses in perovskites, resulting in a natural length scale of around 20 nm for the "effective confining potential" for electrons and holes, with short-range potential fluctuations smoothed out. The increase in Urbach energy across the compositional range agrees well with our optical absorption measurements. We model systems of sizes up to 80 nm in three dimensions, allowing us to accurately reproduce the experimentally observed absorption spectra of perovskites with halide segregation. Our results suggest that we should look beyond static contribution and focus on the dynamic temperature dependent contribution to the Urbach energy.

Functional and structural consequences of epithelial cell invasion by Bordetella pertussis adenylate cyclase toxin

Bordetella pertussis, the causative agent of whopping cough, produces an adenylate cyclase toxin (CyaA) that plays a key role in the host colonization by targeting innate immune cells which express CD11b/CD18, the cellular receptor of CyaA. CyaA is also able to invade non-phagocytic cells, via a unique entry pathway consisting in a direct translocation of its catalytic domain across the cytoplasmic membrane of the cells. Within the cells, CyaA is activated by calmodulin to produce high levels of cyclic adenosine monophosphate (cAMP) and alter cellular physiology. In this study, we explored the effects of CyaA toxin on the cellular and molecular structure remodeling of A549 alveolar epithelial cells. Using classical imaging techniques, biochemical and functional tests, as well as advanced cell mechanics method, we quantify the structural and functional consequences of the massive increase of intracellular cyclic AMP induced by the toxin: cell shape rounding associated to adhesion weakening process, actin structure remodeling for the cortical and dense components, increase in cytoskeleton stiffness, and inhibition of migration and repair. We also show that, at low concentrations (0.5 nM), CyaA could significantly impair the migration and wound healing capacities of the intoxicated alveolar epithelial cells. As such concentrations might be reached locally during B. pertussis infection, our results suggest that the CyaA, beyond its major role in disabling innate immune cells, might also contribute to the local alteration of the epithelial barrier of the respiratory tract, a hallmark of pertussis.

Pathogenesis of chronic rhinosinusitis with nasal polyps: role of IL-6 in airway epithelial cell dysfunction

Background

Chronic rhinosinusitis with nasal polyps (CRSwNP) is characterized by an alteration in airway epithelial cell functions including barrier function, wound repair mechanisms, mucociliary clearance. The mechanisms leading to epithelial cell dysfunction in nasal polyps (NPs) remain poorly understood. Our hypothesis was that among the inflammatory cytokines involved in NPs, IL-6 could alter epithelial repair mechanisms and mucociliary clearance. The aim of this study was to evaluate the in vitro effects of IL-6 on epithelial repair mechanisms in a wound repair model and on ciliary beating in primary cultures of Human Nasal Epithelial Cells (HNEC).

Methods

Primary cultures of HNEC taken from 38 patients during surgical procedures for CRSwNP were used in an in vitro model of wound healing. Effects of increasing concentrations of IL-6 (1 ng/mL, 10 ng/mL, and 100 ng/mL) and other ILs (IL-5, IL-9, IL-10) on wound closure kinetics were compared to cultures without IL-modulation. After wound closure, the differentiation process was characterized under basal conditions and after IL supplementation using cytokeratin-14, MUC5AC, and β_IV tubulin as immunomarkers of basal, mucus, and ciliated cells, respectively. The ciliated edges of primary cultures were analyzed on IL-6 modulation by digital high-speed video-microscopy to measure: ciliary beating frequency (CBF), ciliary length, relative ciliary density, metachronal wavelength and the ciliary beating efficiency index.

Results

Our results showed that: (i) IL-6 accelerated airway wound repair in vitro, with a dose–response effect whereas no effect was observed after other ILs-stimulation. After 24 h, 79% of wounded wells with IL6-100 were fully repaired, vs 46% in the IL6-10 group, 28% in the IL6-1 group and 15% in the control group; (ii) specific migration analyses of closed wound at late repair stage (Day 12) showed IL-6 had the highest migration compared with other ILs (iii) The study of the IL-6 effect on ciliary function showed that CBF and metachronal wave increased but without significant modifications of ciliary density, length of cilia and efficiency index.

Conclusion

The up-regulated epithelial cell proliferation observed in polyps could be induced by IL-6 in the case of prior epithelial damage. IL-6 could be a major cytokine in NP physiopathology.

Deep phenotyping, including quantitative ciliary beating parameters, and extensive genotyping in primary ciliary dyskinesia

Background

Primary ciliary dyskinesia (PCD) is a rare genetic disorder resulting in abnormal ciliary motility/structure, extremely heterogeneous at genetic and ultrastructural levels. We aimed, in light of extensive genotyping, to identify specific and quantitative ciliary beating anomalies, according to the ultrastructural phenotype.

Methods

We prospectively included 75 patients with PCD exhibiting the main five ultrastructural phenotypes (n=15/group), screened all corresponding PCD genes and measured quantitative beating parameters by high-speed video-microscopy (HSV).

Results

Sixty-eight (91%) patients carried biallelic mutations. Combined outer/inner dynein arms (ODA/IDA) defect induces total ciliary immotility, regardless of the gene involved. ODA defect induces a residual beating with dramatically low ciliary beat frequency (CBF) related to increased recovery stroke and pause durations, especially in case of DNAI1 mutations. IDA defect with microtubular disorganisation induces a low percentage of beating cilia with decreased beating angle and, in case of CCDC39 mutations, a relatively conserved mean CBF with a high maximal CBF. Central complex defect induces nearly normal beating parameters, regardless of the gene involved, and a gyrating motion in a minority of ciliated edges, especially in case of RSPH1 mutations. PCD with normal ultrastructure exhibits heterogeneous HSV values, but mostly an increased CBF with an extremely high maximal CBF.

Conclusion

Quantitative HSV analysis in PCD objectives beating anomalies associated with specific ciliary ultrastructures and genotypes. It represents a promising approach to guide the molecular analyses towards the best candidate gene(s) to be analysed or to assess the pathogenicity of the numerous sequence variants identified by next-generation-sequencing.

Surfactant delivery in rat lungs: Comparing 3D geometrical simulation model with experimental instillation

Surfactant Replacement Therapy (SRT), which involves instillation of a liquid-surfactant mixture directly into the lung airway tree, is a major therapeutic treatment in neonatal patients with respiratory distress syndrome (RDS). This procedure has proved to be remarkably effective in premature newborns, inducing a five-fold decrease of mortality in the past 35 years. Disappointingly, its use in adults for treating acute respiratory distress syndrome (ARDS) experienced initial success followed by failures. Our recently developed numerical model has demonstrated that transition from success to failure of SRT in adults could, in fact, have a fluid mechanical origin that is potentially reversible. Here, we present the first numerical simulations of surfactant delivery into a realistic asymmetric conducting airway tree of the rat lung and compare them with experimental results. The roles of dose volume (VD), flow rate, and multiple aliquot delivery are investigated. We find that our simulations of surfactant delivery in rat lungs are in good agreement with our experimental data. In particular, we show that the monopodial architecture of the rat airway tree plays a major role in surfactant delivery, contributing to the poor homogeneity of the end distribution of surfactant. In addition, we observe that increasing VD increases the amount of surfactant delivered to the acini after losing a portion to coating the involved airways, the coating cost volume, VCC. Finally, we quantitatively assess the improvement resulting from a multiple aliquot delivery, a method sometimes employed clinically, and find that a much larger fraction of surfactant reaches the alveolar regions in this case. This is the first direct qualitative and quantitative comparison of our numerical model with experimental studies, which enhances our previous predictions in adults and neonates while providing a tool for predicting, engineering, and optimizing patient-specific surfactant delivery in complex situations.

Universality of fold-encoded localized vibrations in enzymes

Enzymes speed up biochemical reactions at the core of life by as much as 15 orders of magnitude. Yet, despite considerable advances, the fine dynamical determinants at the microscopic level of their catalytic proficiency are still elusive. In this work, we use a powerful mathematical approach to show that rate-promoting vibrations in the picosecond range, specifically encoded in the 3D protein structure, are localized vibrations optimally coupled to the chemical reaction coordinates at the active site. Remarkably, our theory also exposes an hithertho unknown deep connection between the unique localization fingerprint and a distinct partition of the 3D fold into independent, foldspanning subdomains that govern long-range communication. The universality of these features is demonstrated on a pool of more than 900 enzyme structures, comprising a total of more than 10,000 experimentally annotated catalytic sites. Our theory provides a unified microscopic rationale for the subtle structure-dynamics-function link in proteins.

Perfluorocarbon induces alveolar epithelial cell response through structural and mechanical remodeling

During total liquid ventilation, lung cells are exposed to perfluorocarbon (PFC) whose chemophysical properties highly differ from standard aqueous cell feeding medium (DMEM). We herein perform a systematic study of structural and mechanical properties of A549 alveolar epithelial cells in order to characterize their response to PFC exposure, using DMEM as control condition. Changes in F-actin structure, focal adhesion density and glycocalyx distribution are evaluated by confocal fluorescent microscopy. Changes in cell mechanics and adhesion are measured by multiscale magnetic twisting cytometry (MTC). Two different microrheological models (single Voigt and power law) are used to analyze the cell mechanics characterized by cytoskeleton (CSK) stiffness and characteristic relaxation times. Cell-matrix adhesion is analyzed using a stochastic multibond deadhesion model taking into account the non-reversible character of the cell response, allowing us to quantify the adhesion weakness and the number of associated bonds. The roles of F-actin structure and glycocalyx layer are evaluated by depolymerizing F-actin and degrading glycocalyx, respectively. Results show that PFC exposure consistently induces F-actin remodeling, CSK softening and adhesion weakening. These results demonstrate that PFC triggers an alveolar epithelial cell response herein evidenced by a decay in intracellular CSK tension, an adhesion weakening and a glycocalyx layer redistribution. These PFC-induced cell adjustments are consistent with the hypothesis that cells respond to a decrease in adhesion energy at cell surface. This adhesion energy can be even further reduced in the presence of surfactant adsorbed at the cell surface.

IFPA meeting 2017 workshop report: Clinical placentology, 3D structure-based modeling of placental function, placental bed, and treating placental dysfunction

Workshops are an important part of the IFPA annual meeting as they allow for discussion of specialized topics. At IFPA meeting 2017 there were four themed workshops, all of which are summarized in this report. These workshops discussed new knowledge and technological innovations in the following areas of research: 1) placental bed; 2) 3D structural modeling; 3) clinical placentology; 4) treatment of placental dysfunction.

Exposure to Bordetella pertussis adenylate cyclase toxin affects integrin-mediated adhesion and mechanics in alveolar epithelial cells

BACKGROUND INFORMATION

The adenylate cyclase (CyaA) toxin is a major virulent factor of Bordetella pertussis, the causative agent of whooping cough. CyaA toxin is able to invade eukaryotic cells where it produces high levels of cyclic adenosine monophosphate (cAMP) affecting cellular physiology. Whether CyaA toxin can modulate cell matrix adhesion and mechanics of infected cells remains largely unknown.

RESULTS

In this study, we use a recently proposed multiple bond force spectroscopy (MFS) with an atomic force microscope to assess the early phase of cell adhesion (maximal detachment and local rupture forces) and cell rigidity (Young's modulus) in alveolar epithelial cells (A549) for toxin exposure <1 h. At 30 min of exposure, CyaA toxin has a minimal effect on cell viability (>95%) at CyaA concentration of 0.5 nM, but a significant effect (≈81%) at 10 nM. MFS performed on A549 for three different concentrations (0.5, 5 and 10 nM) demonstrates that CyaA toxin significantly affects both cell adhesion (detachment forces are decreased) and cell mechanics (Young's modulus is increased). CyaA toxin (at 0.5 nM) assessed at three indentation/retraction speeds (2, 5 and 10 μm/s) significantly affects global detachment forces, local rupture events and Young modulus compared with control conditions, while an enzymatically inactive variant CyaAE5 has no effect. These results reveal the loading rate dependence of the multiple bonds newly formed between the cell and integrin-specific coated probe as well as the individual bond kinetics which are only slightly affected by the patho-physiological dose of CyaA toxin. Finally, theory of multiple bond force rupture enables us to deduce the bond number N which is reduced by a factor of 2 upon CyaA exposure (N ≈ 6 versus N ≈ 12 in control conditions).

CONCLUSIONS

MFS measurements demonstrate that adhesion and mechanical properties of A549 are deeply affected by exposure to the CyaA toxin but not to an enzymatically inactive variant. This indicates that the alteration of cell mechanics triggered by CyaA is a consequence of the increase in intracellular cAMP in these target cells.

SIGNIFICANCE

These results suggest that mechanical and adhesion properties of the cells appear as pertinent markers of cytotoxicity of CyaA toxin.

A new index for characterizing micro-bead motion in a flow induced by ciliary beating: Part II, modeling

Mucociliary clearance is one of the major lines of defense of the human respiratory system. The mucus layer coating the airways is constantly moved along and out of the lung by the activity of motile cilia, expelling at the same time particles trapped in it. The efficiency of the cilia motion can experimentally be assessed by measuring the velocity of micro-beads traveling through the fluid surrounding the cilia. Here we present a mathematical model of the fluid flow and of the micro-beads motion. The coordinated movement of the ciliated edge is represented as a continuous envelope imposing a periodic moving velocity boundary condition on the surrounding fluid. Vanishing velocity and vanishing shear stress boundary conditions are applied to the fluid at a finite distance above the ciliated edge. The flow field is expanded in powers of the amplitude of the individual cilium movement. It is found that the continuous component of the horizontal velocity at the ciliated edge generates a 2D fluid velocity field with a parabolic profile in the vertical direction, in agreement with the experimental measurements. Conversely, we show than this model can be used to extract microscopic properties of the cilia motion by extrapolating the micro-bead velocity measurement at the ciliated edge. Finally, we derive from these measurements a scalar index providing a direct assessment of the cilia beating efficiency. This index can easily be measured in patients without any modification of the current clinical procedures.

Mucociliary clearance is the first line of defense mechanisms of the human airways. The mucus transporting debris, particles, microorganisms and pollutants is carried away by the coordinated motion of cilia beating at the surface of the airway epithelium. We present here a mathematical and numerical model aiming at defining a global index for assessing the efficiency of this beating. Numerical simulations show that the bead velocity parallel to the wall varies according a parabolic profile with the distance to the wall. The velocity extrapolated at the wall is demonstrated to be a measurement of the momentum transfer between cilia and the surrounding fluid. This model allows us to interpret experimental measurements performed in a companion article and to propose a universal index characterizing the beating efficiency, which can be extracted in the current clinical setting.

A new index for characterizing micro-bead motion in a flow induced by ciliary beating: Part I, experimental analysis

Mucociliary clearance is one of the major lines of defense of the respiratory system. The mucus layer coating the pulmonary airways is moved along and out of the lung by the activity of motile cilia, thus expelling the particles trapped in it. Here we compare ex vivo measurements of a Newtonian flow induced by cilia beating (using micro-beads as tracers) and a mathematical model of this fluid flow, presented in greater detail in a second companion article. Samples of nasal epithelial cells placed in water are recorded by high-speed video-microscopy and ciliary beat pattern is inferred. Automatic tracking of micro-beads, used as markers of the flow generated by cilia motion, enables us also to assess the velocity profile as a function of the distance above the cilia. This profile is shown to be essentially parabolic. The obtained experimental data are used to feed a 2D mathematical and numerical model of the coupling between cilia, fluid, and micro-bead motion. From the model and the experimental measurements, the shear stress exerted by the cilia is deduced. Finally, this shear stress, which can easily be measured in the clinical setting, is proposed as a new index for characterizing the efficiency of ciliary beating.

Studies of the B-Z transition of DNA: The temperature dependence of the free-energy difference, the composition of the counterion sheath in mixed salt, and the preparation of a sample of the 5'-d[T-(m(5) C-G)12 -T] duplex in pure B-DNA or Z-DNA form

It is often envisioned that cations might coordinate at specific sites of nucleic acids and play an important structural role, for instance in the transition between B-DNA and Z-DNA. However, nucleic acid models explicitly devoid of specific sites may also exhibit features previously considered as evidence for specific binding. Such is the case of the "composite cylinder" (or CC) model which spreads out localized features of DNA structure and charge by cylindrical averaging, while sustaining the main difference between the B and Z structures, namely the better immersion of the B-DNA phosphodiester charges in the solution. Here, we analyze the non-electrostatic component of the free-energy difference between B-DNA and Z-DNA. We also compute the composition of the counterion sheath in a wide range of mixed-salt solutions and of temperatures: in contrast with the large difference of composition between the B-DNA and Z-DNA forms, the temperature dependence of sheath composition, previously unknown, is very weak. In order to validate the model, the mixed-salt predictions should be compared to experiment. We design a procedure for future measurements of the sheath composition based on Anomalous Small-Angle X-ray Scattering and complemented by (31) P NMR. With due consideration for the kinetics of the B-Z transition and for the capacity of generating at will the B or Z form in a single sample, the 5'-d[T-(m(5) C-G)12 -T] 26-mer emerges as a most suitable oligonucleotide for this study. Finally, the application of the finite element method to the resolution of the Poisson-Boltzmann equation is described in detail. © 2016 Wiley Periodicals, Inc. Biopolymers 105: 369-384, 2016.

A Macroscopic Model for Simulating the Mucociliary Clearance in a Bronchial Bifurcation: The Role of Surface Tension

The mucociliary clearance in the bronchial tree is the main mechanism by which the lungs clear themselves of deposited particulate matter. In this work, a macroscopic model of the clearance mechanism is proposed. Lubrication theory is applied for thin films with both surface tension effects and a moving wall boundary. The flow field is computed by the use of a finite-volume scheme on an unstructured grid that replicates a bronchial bifurcation. The carina in bronchial bifurcations is of special interest because it is a location of increased deposition of inhaled particles. In this study, the mucus flow is computed for different values of the surface tension. It is found that a minimal surface tension is necessary for efficiently removing the mucus while maintaining the mucus film thickness at physiological levels.

One Single Static Measurement Predicts Wave Localization in Complex Structures

A recent theoretical breakthrough has brought a new tool, called the localization landscape, for predicting the localization regions of vibration modes in complex or disordered systems. Here, we report on the first experiment which measures the localization landscape and demonstrates its predictive power. Holographic measurement of the static deformation under uniform load of a thin plate with complex geometry provides direct access to the landscape function. When put in vibration, this system shows modes precisely confined within the subregions delineated by the landscape function. Also the maxima of this function match the measured eigenfrequencies, while the minima of the valley network gives the frequencies at which modes become extended. This approach fully characterizes the low frequency spectrum of a complex structure from a single static measurement. It paves the way for controlling and engineering eigenmodes in any vibratory system, especially where a structural or microscopic description is not accessible.

Effective Confining Potential of Quantum States in Disordered Media

The amplitude of localized quantum states in random or disordered media may exhibit long-range exponential decay. We present here a theory that unveils the existence of an effective potential which finely governs the confinement of these states. In this picture, the boundaries of the localization subregions for low energy eigenfunctions correspond to the barriers of this effective potential, and the long-range exponential decay characteristic of Anderson localization is explained as the consequence of multiple tunneling in the dense network of barriers created by this effective potential. Finally, we show that Weyl's formula based on this potential turns out to be a remarkable approximation of the density of states for a large variety of one-dimensional systems, periodic or random.

Unsteady diffusional screening in 3D pulmonary acinar structures: from infancy to adulthood

Diffusional screening in the lungs is a physical phenomenon where the specific topological arrangement of alveolated airways of the respiratory region leads to a depletion, or 'screening', of oxygen molecules with increasing acinar generation. Here, we revisit diffusional screening phenomena in anatomically-inspired pulmonary acinar models under realistic breathing maneuvers. By modelling 3D bifurcating alveolated airways capturing both convection and diffusion, unsteady oxygen transport is investigated under cyclic breathing motion. To evaluate screening characteristics in the developing lungs during growth, four representative stages of lung development were chosen (i.e. 3 months, 1 year and 9 months, 3 years and adulthood) that capture distinct morphological acinar changes spanning alveolarization phases to isotropic alveolar growth. Numerical simulations unveil the dramatic changes in O2 transport occurring during lung development, where young infants exhibit highest acinar efficiencies that rapidly converge with age to predictions at adulthood. With increased ventilatory effort, transient dynamics of oxygen transport is fundamentally altered compared to tidal breathing and emphasizes the augmented role of convection. Resolving the complex convective acinar flow patterns in 3D acinar trees allows for the first time a spatially-localized and time-resolved characterization of oxygen transport in the pulmonary acinus, from infancy to adulthood.

The role of morphology in mathematical models of placental gas exchange

The performance of the placenta as a gas exchanger has a direct impact on the future health of the newborn. To provide accurate estimates of respiratory gas exchange rates, placenta models need to account for both the physiology of exchange and the organ morphology. While the former has been extensively studied, accounting for the latter is still a challenge. The geometrical complexity of placental structure requires use of carefully crafted approximations. We present here the state of the art of respiratory gas exchange placenta modeling and demonstrate the influence of the morphology description on model predictions. Advantages and shortcomings of various classes of models are discussed, and experimental techniques that may be used for model validation are summarized. Several directions for future development are suggested.

Multiscale evaluation of cellular adhesion alteration and cytoskeleton remodeling by magnetic bead twisting

Cellular adhesion forces depend on local biological conditions meaning that adhesion characterization must be performed while preserving cellular integrity. We presently postulate that magnetic bead twisting provides an appropriate stress, i.e., basically a clamp, for assessment in living cells of both cellular adhesion and mechanical properties of the cytoskeleton. A global dissociation rate obeying a Bell-type model was used to determine the natural dissociation rate ([Formula: see text]) and a reference stress ([Formula: see text]). These adhesion parameters were determined in parallel to the mechanical properties for a variety of biological conditions in which either adhesion or cytoskeleton was selectively weakened or strengthened by changing successively ligand concentration, actin polymerization level (by treating with cytochalasin D), level of exerted stress (by increasing magnetic torque), and cell environment (by using rigid and soft 3D matrices). On the whole, this multiscale evaluation of the cellular and molecular responses to a controlled stress reveals an evolution which is consistent with stochastic multiple bond theories and with literature results obtained with other molecular techniques. Present results confirm the validity of the proposed bead-twisting approach for its capability to probe cellular and molecular responses in a variety of biological conditions.

A microfluidic model to study fluid dynamics of mucus plug rupture in small lung airways

Fluid dynamics of mucus plug rupture is important to understand mucus clearance in lung airways and potential effects of mucus plug rupture on epithelial cells at lung airway walls. We established a microfluidic model to study mucus plug rupture in a collapsed airway of the 12th generation. Mucus plugs were simulated using Carbopol 940 (C940) gels at concentrations of 0.15%, 0.2%, 0.25%, and 0.3%, which have non-Newtonian properties close to healthy and diseased lung mucus. The airway was modeled with a polydimethylsiloxane microfluidic channel. Plug motion was driven by pressurized air. Global strain rates and shear stress were defined to quantitatively describe plug deformation and rupture. Results show that a plug needs to overcome yield stress before deformation and rupture. The plug takes relatively long time to yield at the high Bingham number. Plug length shortening is the more significant deformation than shearing at gel concentration higher than 0.15%. Although strain rates increase dramatically at rupture, the transient shear stress drops due to the shear-thinning effect of the C940 gels. Dimensionless time-averaged shear stress, T xy , linearly increases from 3.7 to 5.6 times the Bingham number as the Bingham number varies from 0.018 to 0.1. The dimensionless time-averaged shear rate simply equals to T xy /2. In dimension, shear stress magnitude is about one order lower than the pressure drop, and one order higher than yield stress. Mucus with high yield stress leads to high shear stress, and therefore would be more likely to cause epithelial cell damage. Crackling sounds produced with plug rupture might be more detectable for gels with higher concentration.

Analytical theory of oxygen transport in the human placenta

We propose an analytical approach to solving the diffusion-convection equations governing oxygen transport in the human placenta. We show that only two geometrical characteristics of a placental cross-section, villi density and the effective villi radius, are needed to predict fetal oxygen uptake. We also identify two combinations of physiological parameters that determine oxygen uptake in a given placenta: (i) the maximal oxygen inflow of a placentone if there were no tissue blocking the flow and (ii) the ratio of transit time of maternal blood through the intervillous space to oxygen extraction time. We derive analytical formulas for fast and simple calculation of oxygen uptake and provide two diagrams of efficiency of oxygen transport in an arbitrary placental cross-section. We finally show that artificial perfusion experiments with no-hemoglobin blood tend to give a two-orders-of-magnitude underestimation of the in vivo oxygen uptake and that the optimal geometry for such setup alters significantly. The theory allows one to adjust the results of artificial placenta perfusion experiments to account for oxygen-hemoglobin dissociation. Combined with image analysis techniques, the presented model can give an easy-to-use tool for prediction of the human placenta efficiency.

Optimisations and evolution of the mammalian respiratory system : A suggestion of possible gene sharing in evolution

The respiratory system of mammalians is made of two successive branched structures with different physiological functions. The upper structure, or bronchial tree, is a fluid transportation system made of approximately 15 generations of bifurcations leading to the order of about 2(15) = 30, 000 terminal bronchioles with a diameter of approximately 0.5mm in the human lung. The branching pattern continues up to generation 23 but the structure and function of each of the subsequent structures, called acini, is different. Each acinus consists in a branched system of ducts surrounded by alveoli and plays the role of a diffusion cell where oxygen and carbon dioxide are exchanged with blood across the alveolar membrane. We show here that the bronchial tree simultaneously presents several different optimal properties. It is first energy efficient, second, it is space filling and third it is also "rapid". This physically based multi-optimality suggests that, in the course of evolution, an organ selected against one criterion could have been used later for a totally different purpose. For example, once selected for its energetic efficiency for the transport of a viscous fluid like blood, the same genetic material could have been used for its optimized rapidity. This would have allowed the emergence of atmospheric respiration made of inspiration-expiration cycles. For this phenomenon to exist, rapidity is essential as fresh air has to reach the gas exchange organs, the pulmonary acini, before the beginning of expiration. We finally show that the pulmonary acinus is optimized in the sense that the acinus morphology is directly related to the notion of a "best possible" extraction of entropic energy by a diffusion exchanger that has to feed oxygen efficiently from air to blood across a membrane of finite permeability.

An asymptotic model of particle deposition at an airway bifurcation

Particle transport and deposition associated with flow over a wedge is investigated as a model for particle transport and flow at the carina of an airway bifurcation during inspiration. Using matched asymptotics, a uniformly valid solution is obtained to represent the high Reynolds number flow over a wedge that considers the viscous boundary layer near the wedge and the outer inviscid region and is then used to solve the particle transport equations. Sometimes particle impaction on the wedge is prevented due to the boundary layer. We call this boundary layer shielding (BLS). This effect can be broken down into different types: rejection, trapping and deflection that are described by what happens to the particle's initial negative velocity normal to the wall either changing sign, reaching zero, or remaining negative in the boundary layer region. The deposition efficiency depends on the critical Stokes number but exhibits a weak dependence on Reynolds number. Deposition efficiency for S(c) in the range 0 < S(c) < 0.4 yields the following relationship De ≈ (1.867S(c)¹·⁷⁸-0.016) sin(βπ/2) at large Reynolds numbers, where βπ is the wedge angle. For a specific deposition efficiency, S(c) decreases as βπ increases. The distribution of impacted particles was also computed and revealed that particles primarily impact within one airway diameter of the carina, consistent with computational fluid dynamics approaches. This work provides a new insight that the BLS inherent to the wedge component of the structure is the dominant reason for the particle distribution. This finding is important in linking aerosol deposition to the location of airway disease as well as target sites for therapeutic deposition.

Optimal branching asymmetry of hydrodynamic pulsatile trees

Most of the studies on optimal transport are done for steady state regime conditions. Yet, there exists numerous examples in living systems where supply tree networks have to deliver products in a limited time due to the pulsatile character of the flow, as it is the case for mammalian respiration. We report here that introducing a systematic branching asymmetry allows the tree to reduce the average delivery time of the products. It simultaneously increases its robustness against the inevitable variability of sizes related to morphogenesis. We then apply this approach to the human tracheobronchial tree. We show that in this case all extremities are supplied with fresh air, provided that the asymmetry is smaller than a critical threshold which happens to match the asymmetry measured in the human lung. This could indicate that the structure is tuned at the maximum asymmetry level that allows the lung to feed all terminal units with fresh air.

Particle capture into the lung made simple?

Understanding the impact distribution of particles entering the human respiratory system is of primary importance as it concerns not only atmospheric pollutants or dusts of various kinds but also the efficiency of aerosol therapy and drug delivery. To model this process, current approaches consist of increasingly complex computations of the aerodynamics and particle capture phenomena, performed in geometries trying to mimic lungs in a more and more realistic manner for as many airway generations as possible. Their capture results from the complex interplay between the details of the aerodynamic streamlines and the particle drag mechanics in the resulting flow. In contrast, the present work proposes a major simplification valid for most airway generations at quiet breathing. Within this context, focusing on particle escape rather than capture reveals a simpler structure in the entire process. When gravity can be neglected, we show by computing the escape rates in various model geometries that, although still complicated, the escape process can be depicted as a multiplicative escape cascade in which each elementary step is associated with a single bifurcation. As a net result, understanding of the particle capture may not require computing particle deposition in the entire lung structure but can be abbreviated in some regions using our simpler approach of successive computations in single realistic bifurcations. Introducing gravity back into our model, we show that this multiplicative model can still be successfully applied on up to nine generations, depending on particle type and breathing conditions.

An anatomical and functional model of the human tracheobronchial tree

The human tracheobronchial tree is a complex branched distribution system in charge of renewing the air inside the acini, which are the gas exchange units. We present here a systematic geometrical model of this system described as a self-similar assembly of rigid pipes. It includes the specific geometry of the upper bronchial tree and a self-similar intermediary tree with a systematic branching asymmetry. It ends by the terminal bronchioles whose generations range from 8 to 22. Unlike classical models, it does not rely on a simple scaling law. With a limited number of parameters, this model reproduces the morphometric data from various sources (Horsfield K, Dart G, Olson DE, Filley GF, Cumming G. J Appl Physiol 31: 207-217, 1971; Weibel ER. Morphometry of the Human Lung. New York: Academic Press, 1963) and the main characteristics of the ventilation. Studying various types of random variations of the airway sizes, we show that strong correlations are needed to reproduce the measured distributions. Moreover, the ventilation performances are observed to be robust against anatomical variability. The same methodology applied to the rat also permits building a geometrical model that reproduces the anatomical and ventilation characteristics of this animal. This simple model can be directly used as a common description of the entire tree in analytical or numerical studies such as the computation of air flow distribution or aerosol transport.

Strong localization induced by one clamped point in thin plate vibrations

We discover a strong localization of flexural (bi-Laplacian) waves in rigid thin plates. We show that clamping just one point inside such a plate not only perturbs its spectral properties, but essentially divides the plate into two independently vibrating regions. This effect progressively appears when increasing the plate eccentricity. Such a localization is qualitatively and quantitatively different from the results known for the Laplacian waves in domains of irregular boundary. It would allow us to control the confinement of mechanical vibrations in rigid plates and of eddies in the slow Stokes flow.

Role of diffusion screening in pulmonary diseases

It has been shown recently that the acinus is only partially efficient in normal conditions. This is due to a "screening effect" governed by the relative values of the oxygen diffusivity and the membrane resistance as well as design and size of the acinus. These effects depend on the fraction of the acinus in which gas transport is governed by diffusion, then on the location of the convection-diffusion transition. It is shown that these screening effects gives to respiration at rest a partial protection against several types of pulmonary diseases. This is true for mild emphysema, mild asthma or COPD and mild edema. In contrast, under exercise respiration, the acinus is totally efficient and the protective effects linked to the existence of screening do not exist anymore.

Screening effects in flow through rough channels

A surprising similarity is found between the distribution of hydrodynamic stress on the wall of an irregular channel and the distribution of flux from a purely Laplacian field on the same geometry. This finding is a direct outcome of numerical simulations of the Navier-Stokes equations for flow at low Reynolds numbers in two-dimensional channels with rough walls presenting either deterministic or random self-similar geometries. For high Reynolds numbers, the distribution of wall stresses on deterministic and random fractal rough channels becomes substantially dependent on the microscopic details of the walls geometry. Finally, the effects on the flow behavior of the channel symmetry and aspect ratio are also investigated.

Mathematical basis for a general theory of Laplacian transport towards irregular interfaces

The theory of Laplacian transport towards and across irregular surfaces is reformulated in terms of the Dirichlet-to-Neumann operator and its spectral characteristics. This permits us to obtain an exact equivalent circuit for the impedance of a working interface of arbitrary shape. The important result is that only very few eigenmodes of this operator do govern the entire response of a macroscopic system. This property drastically simplifies the understanding of irregular or prefractal interfaces. The results can be applied in electrochemistry, physiology and chemical engineering, fields where exchange processes across surfaces with complex geometry are ubiquitous.

Design of peripheral airways for efficient gas exchange

Peripheral airways combine branched tubes for ventilation with the gas exchanging alveoli in the pulmonary acini, defined as the complex of airways supplied by one first order respiratory or transitional bronchiole. In this part, the replenishment of oxygen at the alveolar surface occurs by a combination of convective air flow with diffusion of oxygen in the air. The transition between convection and diffusion depends on the morphometric properties of the airways. The design of the peripheral airways in the acinus of the human lung is described quantitatively on the basis of measurements obtained on casts of the acinar airways. Comparable data for rat and rabbit are also discussed. On the basis of this morphometric information, a typical path model for human acinar airways is derived. These studies also form the basis for advanced modeling studies of gas exchange and ventilation. In particular the problems occurring because of diffusional screening and the design conditions for minimizing this effect are discussed.

Diffusional screening in real 3D human acini--a theoretical study

Gas exchange at the acinar level involves several physico-chemical phenomena within a complex geometry. A gas transport model, which takes into account both the diffusion into the acinus and the diffusion across the alveolar membrane, is used to understand gas mixing in realistic systems. It is first shown that the behaviour of the system, computed on model geometries in 3D, only depends on the topological structure of the acinus. Taking advantage of this property, a new efficient method based on random walks on a lattice is used to compute gas diffusion in structures taken from real morphological data. This approach shows that, at rest, the human acinus efficiency is only 30-40%. These results provide a new evidence of the existence of diffusional screening at the acinar level. This implies permanent spatial inhomogeneity of oxygen and carbon dioxide partial pressure. The notion of an "alveolar gas" is reinterpreted as a spatial average of the gas distribution. This model casts new light on the respiratory properties of other gas mixtures, such as helium-oxygen.

Multifractal properties of the harmonic measure on Koch boundaries in two and three dimensions

The multifractal properties of the harmonic measure on quadratic and cubic Koch boundaries are studied with the help of a new fast random walk algorithm adapted to these fractal geometries. The conjectural logarithmic development of local multifractal exponents is guessed for regular fractals and checked by extensive numerical simulations. This development allows one to compute the multifractal exponents of the harmonic measure with high accuracy, even with the first generations of the fractal. In particular, the information dimension in the case of the concave cubic Koch surface embedded in three dimensions is found to be slightly higher than its value D1 =2 for a smooth boundary.

Diffusion-reaction in branched structures: theory and application to the lung acinus

An exact "branch by branch" calculation of the diffusional flux is proposed for partially absorbed random walks on arbitrary tree structures. In the particular case of symmetric trees, an explicit analytical expression is found which is valid whatever the size of the tree. Its application to the respiratory phenomena in pulmonary acini gives an analytical description of the crossover regime governing the human lung efficiency.

Cancer death statistics: analogy between epidemiology and critical systems in physics

The determination of risk factors in carcinogenesis is said to be an essential step towards the understanding of this disease. Most mathematical models describing the evolution of mortality figures use the concept of death probability (or "force of mortality" or "hazard of death"). When summarizing the death statistics through this unique parameter, one implicitly makes the assumption that the death events are independent from one individual to another. In this paper, we show that this hypothesis has profound consequences as it implies a "gaussian" behavior of the death statistics fluctuations. In order to verify the validity of this assumption, French cancer death statistics between the years 1978-1996 are examined. Their fluctuations, for every age bracket, are computed and then compared to the expected gaussian fluctuations that should emerge from a model of death probability. We show that the observed fluctuations are in close agreement with a gaussian model up to 35-40 years. After 40 years, the fluctuations are much higher and cannot be explained by a model where every individual would have a given "probability of death". These observations may produce a new insight into old-age cancer mortality. It suggests that there could exist a major difference between cancers in young or older organisms: cancer developed in young organisms are the consequence of a specific attack against an organ (essentially originated from a single cause, like a virus or a genetic deficiency). On the other hand, older organism are closer to a "critical state" and, as such, the outcome of a cancer in a given organ could be the consequence of a chain of "malfunctions" (analogous to an avalanche in physical systems) in the entire organism.

An optimal bronchial tree may be dangerous

The geometry and dimensions of branched structures such as blood vessels or airways are important factors in determining the efficiency of physiological processes. It has been shown that fractal trees can be space filling and can ensure minimal dissipation. The bronchial tree of most mammalian lungs is a good example of an efficient distribution system with an approximate fractal structure. Here we present a study of the compatibility between physical optimization and physiological robustness in the design of the human bronchial tree. We show that this physical optimization is critical in the sense that small variations in the geometry can induce very large variations in the net air flux. Maximum physical efficiency therefore cannot be a sufficient criterion for the physiological design of bronchial trees. Rather, the design of bronchial trees must be provided with a safety factor and the capacity for regulating airway calibre. Paradoxically, our results suggest that bronchial malfunction related to asthma is a necessary consequence of the optimized efficiency of the tree structure.

Renormalized random walk study of oxygen absorption in the human lung

The possibility to renormalize random walks is used to study numerically the oxygen diffusion and permeation in the acinus, the diffusion cell terminating the mammalian airway tree. This is done in a 3D tree structure which can be studied from its topology only. The method is applied to the human acinus real morphology as studied by Haefeli-Bleuer and Weibel in order to compute the respiratory efficiency of the human lung. It provides the first quantitative evidence of the role of diffusion screening in real 3D mammalian respiration. The net result of this study is that, at rest, the efficiency of the human acinus is only of order 33%. Application of these results to CO2 clearance provides for the first time a theoretical support to the empirical relation between the O2 and CO2 partial pressures in blood.

Diffusional screening in the human pulmonary acinus

In the mammalian lung acini, O(2) diffuses into quasi-static air toward the alveolar membrane, where the gas exchange with blood takes place. The O(2) flux is then influenced by the O(2) diffusivity, the membrane permeability, and the acinus geometric complexity. This phenomenon has been recently studied in an abstract geometric model of the acinus, the Hilbert acinus (Sapoval B, Filoche M, and Weibel ER, Proc Natl Acad Sci USA 99: 10411, 2002). This is extended here to a more realistic geometry originated from the morphological model of Kitaoka et al. (Kitaoka K, Tamura S, and Takaki R, J Appl Physiol 88: 2260-2268, 2000). Two-dimensional numerical simulations of the steady-state diffusion equation with mixed boundary conditions are used to quantify the process. The alveolar O(2) concentration, or partial pressure, and the O(2) flux are computed and show that diffusional screening exists at rest. These results confirm that smaller acini are more efficient, as suggested for the Hilbert acini.

Interplay between geometry and flow distribution in an airway tree

Uniform flow distribution in a symmetric volume can be realized through a symmetric branched tree. It is shown here, however, by 3D numerical simulation of the Navier-Stokes equations, that the flow partitioning can be highly sensitive to deviations from exact symmetry if inertial effects are present. The flow asymmetry is quantified and found to depend on the Reynolds number. Moreover, for a given Reynolds number, we show that the flow distribution depends on the aspect ratio of the branching elements as well as their angular arrangement. Our results indicate that physiological variability should be severely restricted in order to ensure adequate fluid distribution through a tree.

Smaller is better--but not too small: a physical scale for the design of the mammalian pulmonary acinus

The transfer of oxygen from air to blood in the lung involves three processes: ventilation through the airways, diffusion of oxygen in the air phase to the alveolar surface, and finally diffusion through tissue into the capillary blood. The latter two steps occur in the acinus, where the alveolar gas-exchange surface is arranged along the last few generations of airway branching. For the acinus to work efficiently, oxygen must reach the last branches of acinar airways, even though some of it is absorbed along the way. This "screening effect" is governed by the relative values of physical factors like diffusivity and permeability as well as size and design of the acinus. Physics predicts that efficient acini should be space-filling surfaces and should not be too large. It is shown that the mammalian acini fulfill these requirements, small mammals being more efficient than large ones both at rest and in exercise.