Benjamin Mauroy

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, θp0, 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

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.

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 placentas 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.

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.

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.

Murray's law revisited: Quémada's fluid model and fractal trees

We investigate how Murrays law is affected by fluids whose viscosity depends monotonously on shear rates, such as blood. Our study shows that Murrays original law also applies to such fluids, as long as they did not undergo phase separation effect. When Fahraeus-like phase separation effects occur, we derive an extended version of Murrays law. Finally, we study how these new laws affect the optimal geometries of fractal trees to mimic an idealized arterial network. Our analyses are based on Quemadas fluid model, but our approach is very general and applied to most fluids with shear dependent rheology.

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 lungs 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.

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.

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 models 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 models 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.

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.