Why do myofibroblasts preferentially accumulate on the convex surface of the remodeling lung after pneumonectomy?

Myofibroblasts preferentially accumulate on the convex and not on the concave surfaces of the murine cardiac lobe during lung remodeling after pneumonectomy. This clear difference in function due to the organ shape is most likely mediated by the various mechanical forces generated on the lung's surface. For breathing, the lobe cyclically change its configuration. The cyclic deformation requires energy, depending on the local configuration of the lobe (e.g., convex vs. concave). Considering mechanical contributions to the internal energy of the system and according to the second law of thermodynamics, the system seeks the lowest energy state for equilibrium. Although additional energy for remodeling is required, the system chooses such remodeling sites that minimize the total energy of the new equilibrium state. To test this idea, an idealized, concave-convex configuration of the lobe is assumed. The lobe is made of two homogeneous and isotropic materials of different mechanical properties, the bulk parenchyma and the pleura, a thin, mesothelial cell layer surrounding it. While the whole system cyclically changes shape during breathing, we calculated the amount of mechanical energy per unit volume at the parenchyma-pleural interface where, we believe, myofibroblasts preferentially accumulate. Comparison between convex and concave surfaces indicates that convex surfaces store a lower amount of mechanical energy than the concave ones. We also show that any additional energy for remodeling is preferably done at the convex surface where the lowest new energy equilibrium state is achieved.

Alveolar septal patterning during compensatory lung growth: Part II the effect of parenchymal pressure gradients.

In most mammals, compensatory lung growth occurs after the removal of one lung (pneumonectomy). Although the mechanism of alveolar growth is unknown, the patterning of complex alveolar geometry over organ-sized length scales is a central question in regenerative lung biology. Because shear forces appear capable of signaling the differentiation of important cells involved in neoalveolarization (fibroblasts and myofibroblasts), interstitial fluid mechanics provide a potential mechanism for the patterning of alveolar growth. The movement of interstitial fluid is created by two basic mechanisms: 1) the non-uniform motion of the boundary walls, and 2) parenchymal pressure gradients external to the interstitial fluid. In a previous study (Haber et al., Journal of Theoretical Biology 400: 118-128, 2016), we investigated the effects of non-uniform stretching of the primary septum (associated with its heterogeneous mechanical properties) during breathing on generating non-uniform Stokes flow in the interstitial space. In the present study, we analyzed the effect of parenchymal pressure gradients on interstitial flow. Dependent upon lung microarchitecture and physiologic conditions, parenchymal pressure gradients had a significant effect on the shear stress distribution in the interstitial space of primary septa. A dimensionless parameter δ described the ratio between the effects of a pressure gradient and the influence of non-uniform primary septal wall motion. Assuming that secondary septa are formed where shear stresses were the largest, it is shown that the geometry of the newly generated secondary septa was governed by the value of δ. For δ smaller than 0.26, the alveolus size was halved while for higher values its original size was unaltered. We conclude that the movement of interstitial fluid, governed by parenchymal pressure gradients and non-uniform primary septa wall motion, provides a plausible mechanism for the patterning of alveolar growth.

Interstitial fluid flow of alveolar primary septa after pneumonectomy.

Neoalveolation is known to occur in the remaining lung after pneumonectomy. While compensatory lung growth is a complex process, stretching of the lung tissue appears to be crucial for tissue remodeling. Even a minute shear stress exerted on fibroblasts in the interstitial space is known to trigger cell differentiation into myofibroblast that are essential to building new tissues. We hypothesize that the non-uniform motion of the primary septa due to their heterogeneous mechanical properties under tidal breathing induces a spatially unique interstitial flow and shear stress distribution in the interstitial space. This may in turn trigger pulmonary fibroblast differentiation and neoalveolation. In this study, we developed a theoretical basis for how cyclic motion of the primary septal walls with heterogeneous mechanical properties affects the interstitial flow and shear stress distribution. The velocity field of the interstitial flow was expressed by a Fourier (complex) series and its leading term was considered to induce the basic structure of stress distribution as long as the dominant length scale of heterogeneity is the size of collapsed alveoli. We conclude that the alteration of mechanical properties of the primary septa caused by pneumonectomy can develop a new interstitial flow field, which alters the shear stress distribution. This may trigger the differentiation of resident fibroblasts, which may in turn induce spatially unique neoalveolation in the remaining lung. Our example illustrates that the initial forming of new alveoli about half the size of the original ones.

Blood flow in capillaries of the human lung.

A novel model for the blood system is postulated focusing on the flow rate and pressure distribution inside the arterioles and venules of the pulmonary acinus. Based upon physiological data it is devoid of any ad hoc constants. The model comprises nine generations of arterioles, venules, and capillaries in the acinus, the gas exchange unit of the lung. Blood is assumed incompressible and Newtonian and the blood vessels are assumed inextensible. Unlike previous models of the blood system, the venules and arterioles open up to the capillary network in numerous locations along each generation. The large number of interconnected capillaries is perceived as a porous medium in which the flow is macroscopically unidirectional from arterioles to venules openings. In addition, the large number of capillaries extending from each arteriole and venule allows introduction of a continuum theory and formulation of a novel system of ordinary, nonlinear differential equations which governs the blood flow and pressure fields along the arterioles, venules, and capillaries. The solution of the differential equations is semianalytical and requires the inversion of three diagonal, 9 × 9 matrices only. The results for the total flow rate of blood through the acinus are within the ballpark of physiological observations despite the simplifying assumptions used in our model. The results also manifest that the contribution of the nonlinear convection term of the Navier-Stokes equations has little effect (less than 2%) on the total blood flow entering/leaving the acinus despite the fact that the Reynolds number is not much smaller than unity at the proximal generations. The model makes it possible to examine some pathological cases. Here, centri-acinar and distal emphysema were investigated yielding a reduction in inlet blood flow rate.

Trajectories and deposition sites of spherical particles moving inside rhythmically expanding alveoli under gravity-free conditions.

BACKGROUND: Do fine particles (0.5-2 µm in diameter) deposit inside lung alveoli? This question is of particular interest in space flights where almost gravity-free conditions exist. Under such conditions, inhaled particles smaller than 0.5 µm in diameter or larger than 2 µm may deposit inside the alveoli due to Brownian motion or particle inertia, respectively. However, fine particles hardly affected by Brownian motion and of small mass can (wrongly) be perceived harmless, following closely fluid pathlines. METHODS: The interplay between alveoli rhythmical expansion and the largely, previously disregarded geometrical interception mechanism was explored vis-à-vis predictions based on nonexpanding alveoli models. To this end, we employed a three-dimensional flow model that accounts for the rhythmical expansion of alveoli, and the trajectories of fine particles embedded in this flow were numerically calculated. RESULTS: Stochastic trajectories and deposition sites that are substantially different than those obtained for reversible Poiseuille-like flow models were widely used in the past. Indeed, small, inertialess, non-Brownian particles can hardly enter rigid alveoli in microgravity circumstances because the flow field consists of isolated closed streamlines that separate the cavities from the airways. However, for expanding alveoli, the streamline map is significantly altered, allowing diversion of particles from the airways toward the alveoli walls. As a result, collision with the alveoli wall due to geometrical interception may occur, revealing an additional mechanism that may control particle deposition inside alveoli. CONCLUSIONS: Fine particles 0.5-2 µm in diameter under zero gravity conditions may enter expanding alveoli and deposit due to the stochastic nature of the flow and the mechanism of geometrical interception. Their fate is very sensitive to their initial position. The majority of the particles tend to deposit inside alveoli located up the acinar tree, at the distal area of the alveoli and near its rim.

Propagation and breakup of liquid menisci and aerosol generation in small airways.

BACKGROUND: Droplets exhaled during normal breathing and not associated with coughing may pose hazardous agents to infective diseases dissemination. The objective is to explore the physical mechanism, which may lead to droplets formation. METHODS: We hypothesize that liquid menisci occlusions, which may form inside small airways, travel along the airway, may lose mass and finally disintegrate into small droplets. This hypothesis was numerically investigated applying physiologically plausible values of the phenomenological coefficients and geometrical conformations. RESULTS: We show that three important dimensionless parameters control the motion and disintegration of menisci: the dimensionless mucus layer thickness, the dimensionless menisci initial thickness (all scaled by the airway radius), and the capillary number. Menisci traveling within airways may either remain at equilibrium or diminish or increase in size. Menisci that diminish in size may collapse into the mucus layer; form a large droplet that contains most of the menisci mass before disintegration; or form a larger number of small droplets (we show the forming of three or four droplets in a single occluded airway). CONCLUSIONS: A critical capillary number for menisci at equilibrium could be defined. It was shown that menisci tend to diminish in size as the capillary number increases above the critical value, and a number of small droplets may be formed during normal breathing.

Density-induced coupling effects on the dispersivity of a flexible chain particle.

A model is introduced to investigate the transport properties of an inhomogeneously dense flexible chain particle. The specific model used is a sedimenting non-neutrally buoyant inhomogenously weighted flexible Brownian dumbbell, and it is shown that density inhomogeneity gives rise to a novel coupling effect between the "shape-fluctuation" and "size-fluctuation" dispersion mechanisms. The previously reported shape-fluctuation dispersion term stems from the dumbbell's nonspherical shape and the ensuing anisotropic mobility tensor, while the already investigated size fluctuation term is the result of the dependence of the overall dumbbell translational mobility on the separation distance between the constitutive spheres. Because the density of the constitutive spheres is unequal, the external force simultaneously reorients and deforms the flexible dumbbell, and it is this mutual dependence between dumbbell orientation and size that induces the coupling. Numerical results are presented for the case of a tethered dumbbell composed of two spheres, identical in size but differing in density. The "weak-field" limit is addressed, where the externally applied torque and particle deformation forces are dominated by the thermal fluctuations associated with rotational and deformation Brownian motion. This numerical solution, obtained by including a large number of higher order hydrodynamic interactions (120 terms), describes the Brownian particle's long-time transport without resorting to ad hoc approximations, such as preaveraging the hydrodynamic force or incorporating only first-order hydrodynamic interaction effects (such as employing the Burgers-Oseen tensor). Separate analytical solutions, based on these respective approximations, are also presented and it is concluded that in the limit of "long tethers," where the ratio of tether length to sphere size is greater than seven, no more than 15% error is introduced by neglecting higher-order hydrodynamic interactions. Similarly, the preaveraging approximation introduces no more than a few percent error in the limit of "almost-rigid" dumbbells, where the ratio of tether length to sphere size is less than three. For tethers of "intermediate" length, the full numerical solution must be employed.