Slow viscous flow in a lung alveoli model

The permeability of pillar arrays in microfluidic devices: an application of Brinkman's theory towards wall friction

Darcy's law describes the flow of Newtonian fluids through bulk porous media as the product of the applied pressure difference, the fluid's viscosity and the medium's permeability. Brinkman extended Darcy's law with a viscous stress term, thereby enabling boundary conditions to the flow field at the surface of the medium. The validity of Brinkman's term, and the value of its effective viscosity, have been heavily debated since their introduction nearly 75 years ago. We use experiments and Multibody Dissipative Particle Dynamics (MDPD) simulations to study flows through ordered and disordered pillar arrays in microfluidic channels of limited height. We find that the simulated velocity profiles are well described by an expedient interpretation of Brinkman's theory. Depending on the solid volume fraction and pillar arrangement, the effective viscosity varies between two and three times the bulk fluid viscosity. The calculated effective permeabilities of the flow devices, combining the flow resistances due to the pillars and the walls by Brinkman's theory, agree well with the experimental data. This approach enables fast and accurate estimates of the effective permeability of micropillared chips. The simulated force distributions over the walls and pillars require an effective viscosity equal to the bulk viscosity and an elevation-dependent permeability of the pillar array.

Microvascular fluid flow in ex vivo and engineered lungs

In recent years, it has become common to experiment with ex vivo perfused lungs for organ transplantation and to attempt regenerative pulmonary engineering using decellularized lung matrices. However, our understanding of the physiology of ex vivo organ perfusion is imperfect; it is not currently well understood how decreasing microvascular barrier affects the perfusion of pulmonary parenchyma. In addition, protocols for lung perfusion and organ culture fluid-handling are far from standardized, with widespread variation on both basic methods and on ideally controlled parameters. To address both of these deficits, a robust, noninvasive, and mechanistic model is needed which is able to predict microvascular resistance and permeability in perfused lungs while providing insight into capillary recruitment. Although validated mathematical models exist for fluid flow in native pulmonary tissue, previous models generally assume minimal intravascular leak from artery to vein and do not assess capillary bed recruitment. Such models are difficult to apply to both ex vivo lung perfusions, in which edema can develop over time and microvessels can become blocked, and to decellularized ex vivo organomimetic cultures, in which microvascular recruitment is variable and arterially perfused fluid enters into the alveolar space. Here, we develop a mathematical model of pulmonary microvascular fluid flow which is applicable in both instances, and we apply our model to data from native, decellularized, and regenerating lungs under ex vivo perfusion. The results provide substantial insight into microvascular pressure-flow mechanics, while producing previously unknown output values for tissue-specific capillary-alveolar hydraulic conductivity, microvascular recruitment, and total organ barrier resistance.NEW & NOTEWORTHY We present a validated model of pulmonary microvascular fluid mechanics and apply this model to study the effects of increased capillary permeability in decellularized and regenerating lungs. We find that decellularization alters microvascular steady-state mechanics and that re-endothelialization partially rescues key biologic parameters. The described model provides powerful insight into intraorgan microvascular dynamics and may be used to guide regenerative engineering experiments. We include all data and derivations necessary to replicate this work.

Microchannel technologies for artificial lungs: (1) theory

The feasibility of developing micro channel artificial lungs is calculated for eight possible strategies: 12 and 25 microm circular channels imbedded in gas-permeable sheets, 12 and 25 microm high open rectangular channels with gas-permeable walls, 12 and 25 microm high broad open channels with support posts and gas-permeable walls, and two 40 microm high screen-filled rectangular channels with gas-permeable walls. Each strategy is considered by imposing a pressure drop maximum of 10 mm Hg and limiting the possibility of shear-induced blood trauma. The pressure drop limit determines the acceptable channel length and required size to oxygenate 4 L/min of venous blood. Circular channels imbedded in open-pore, gas-permeable materials are especially attractive. With 12 microm channels, such a device would require 140 million, 0.8 mm long channels, but the total size of the gas-exchange section would be only 57 ml and a blood prime of only 13 ml. Also attractive are 12 mum high broad open channels with support posts and 40 mum screen-filled rectangular channels. The total size of the former would be 250 ml with a blood prime of 13 ml, and the total size of the latter would be 270 ml with a blood prime of 27 ml.

Microchannel technologies for artificial lungs: (3) open rectangular channels

Lithographic techniques were used to develop patterned silicone rubber membranes that provide 15 microm high microchannels for artificial lungs. Two types of devices were fabricated as a proof-of-concept: one has a series of parallel, straight, open rectangular channels that are each 300 microm wide, separated by 200-microm walls, and 3-mm long and the other is a wide rectangular channel with support posts, also 3- mm long. Experiments with 30% hematocrit, venous, bovine blood showed average oxygen fluxes ranging from 11 x 10(-7) moles/(min x cm(2)) at a residence time of 0.04 sec to 6.5 x 10(-7) moles/(min x cm(2)) at a residence time of 0.20 sec. The average oxygen flux vs. residence time, which is due to transverse molecular diffusion, follows the same relation for all membranes tested. The corresponding increase in hemoglobin saturation ranged from 9% at the residence time of 0.04 sec to 24% at the residence time of 0.20 sec. The support-post channel membranes are attractive for designers because they can be arbitrarily wide and would be less prone to blockage.

Microcirculation impedance analysis in cat lung

An analysis of pulsatile microcirculation in cat lung, with special attention to the pulmonary microvascular impedance, is presented. A theoretical calculation is made on the basis of a complete set of experimental data on the morphology and elasticity of cat's pulmonary capillary sheets. The transfer matrix of the pulmonary microvascular impedance is obtained. The input impedance at the capillary entrance and exit are determined. The input impedance at the pulmonary arterial trunk is compared under various physiological conditions. It is shown that although the impact of pulmonary microcirculation on the relationship between the steady mean flow and pressure in the pulmonary arteries and veins is decisively large, the influence of the alveolar microcirculation on the input impedance at the pulmonary arterial trunk is small.

A three-dimensional junction-pore-matrix model for capillary permeability

A three-dimensional model is presented for the hydraulic conductivity and diffusive permeability of capillary endothelial clefts with a junctional strand with discrete pores and a fiber matrix in its wide parts. The model attempts to provide new insight into long-standing issues concerning the relative importance of open junction discontinuities, restricted slit regions, and matrix components in determining the permeability and selectivity of the capillary wall. The predictions drawn from the model are used to formulate new experiments to test two hypotheses concerning the molecular organization of the junction strand and the location of matrix structures in the wide part of the cleft. Using the three-dimensional theoretical approach recently developed by Tsay, Weinbaum, and Pfeffer (Chem. Eng. Comm. 82, 67-102, 1989), the model first explores the behavior of three different molecular models for the junctional strand discontinuities: (i) a more frequent circular pore of 5.5-nm radius formed by isolated missing junction proteins; (ii) a restricted rectangular slit of four to eight missing proteins and 8-nm gap height; and (iii) larger more infrequent breaks of four to eight missing proteins with a gap height of 22 nm, equal to the width of the wide part of the cleft. For the circular and 8-nm gap height pores the primary molecular sieve can be located at the level of the junction strand, whereas for the 22-nm gap height pores, matrix components must be present in at least some portion of the cleft to provide the molecular filter. The water flow through the cross-bridging fibers in the wide part of the cleft is described either by a new exact three-dimensional theory (Tsay and Weinbaum, J. Fluid Mech. 226, 125-148, 1991) for an ordered periodic array or by a new approximate theory for a random array of perpendicular fibers. Both this theory and the new approximate theory for diffusion presented herein take into account for the first time the interaction between the fibers and plasmalemma boundaries. The principal predictions of the model are that (i) infrequent larger breaks are most likely required to account for small solute permeability; (ii) these larger breaks must be accompanied by a sieving matrix, but this matrix probably occupies only a small portion of the depth of the cleft and/or its entrance at the luminal surface; (iii) neither junctional pore, restricted slit, or fiber matrix models can by themselves satisfy permeability and selectivity data; and (iv) one-dimensional models are a poor description of a cleft with infrequent larger breaks since the solute will be confined to small wakelike regions on the downstream side of the junction strand discontinuities and thus not fill the wide part of the cleft.

Pulmonary alveolar blood flow

Explicit results concerning blood flow, alveolar blood volume, regional differences, and transit time distribution are derived from the sheet-flow theory and compared with experimental evidence available in the literature. A general consistency is indicated. The theory exhibits in a simple form the effects on flow of the arterial, alveolar, and venous pressures, the alveolar area, the mean path length between arterioles and venules, and the tension in the alveolar membrane, both elastic and surface tension; thus the theory provides a quantitative understanding of a large number of factors.