Stefan Gheorghiu

Is the Lung an Optimal Gas Exchanger

We investigate gas transport and exchange in a model of the mammalian lung, from the perspective of thermodynamic optimization (second law energy efficiency). This approach to modeling the structure-function relation of the lung exploits the analogy between the respiratory organs and a chemical membrane reactor, and reveals that the design of the lung may be optimal for its function. We use methods from irreversible thermodynamics to give approximate expressions for the entropy production rate in the lung, and a variational approach to minimize the rate under meaningful functional constraints. The large-scale bronchial tree and small-scale alveolar sponge are modeled separately, to account for the different nature of mass-transport at the two scales (pressure-driven flow and diffusion, respectively). We prove that maximum energy efficiency requires equipartition of thermodynamic forces: pressure drop must be uniformly distributed across all the branches of the bronchial tree, and oxygen concentration drop must be uniformly distributed over the lung membrane. We show that the fractal-like architecture of the lung, the particular size of the gas-exchange units, and the subtle interplay between the airway tree and its vascular network are highly compatible with these requirements of equipartition.

Gas Diffusion through the Fractal Landscape of the Lung: How Deep Does Oxygen Enter the Alveolar System?

We investigate oxygen transport to and across alveolar membranes in the human lung, the last step in the chain of events that takes oxygen through the bronchial airways to the peripheral, acinar airways. This step occurs by diffusion. We carry out analytic and numerical computations of the oxygen current for fractal, space-filling models of the acinus, based on morphological data of the acinus and appropriate values for the transport constants, without adjustable parameters. The computations address the question whether incoming oxygen reaches the entire available membrane surface (reaction-limited, unscreened oxygen current), a large part of the surface (mixed reaction/diffusion-limited, partly screened current), or only the surface near the entrance of the acinus (diffusion-limited, completely screened current). The analytic treatment identifies the three cases as sharply delineated screening regimes and finds that the lung operates in the partial-screening regime, close to the transition to no screening, for respiration at rest; and in the no-screening regime for respiration at exercise. The resulting currents agree well with experimental values. We test the analytic treatment by comparing it with numerical results for two-dimensional acinus models and find very good agreement. The results provide quantitative support for the conclusion, obtained in other work, that the space-filling fractal architecture of the lung is optimal with respect to active membrane surface area and minimum power dissipation. At the level of the bronchial tree, we show that the space-filling architecture provides optimal slowing down of the airflow from convection in the bronchial airways to diffusion in the acinar airways.

Reverse Engineering of Oxygen Transport in the Lung: Adaptation to Changing Demands and Resources through Space-Filling Networks

The space-filling fractal network in the human lung creates a remarkable distribution system for gas exchange. Landmark studies have illuminated how the fractal network guarantees minimum energy dissipation, slows air down with minimum hardware, maximizes the gas- exchange surface area, and creates respiratory flexibility between rest and exercise. In this paper, we investigate how the fractal architecture affects oxygen transport and exchange under varying physiological conditions, with respect to performance metrics not previously studied. We present a renormalization treatment of the diffusion-reaction equation which describes how oxygen concentrations drop in the airways as oxygen crosses the alveolar membrane system. The treatment predicts oxygen currents across the lung at different levels of exercise which agree with measured values within a few percent. The results exhibit wide-ranging adaptation to changing process parameters, including maximum oxygen uptake rate at minimum alveolar membrane permeability, the ability to rapidly switch from a low oxygen uptake rate at rest to high rates at exercise, and the ability to maintain a constant oxygen uptake rate in the event of a change in permeability or surface area. We show that alternative, less than space-filling architectures perform sub-optimally and that optimal performance of the space-filling architecture results from a competition between underexploration and overexploration of the surface by oxygen molecules.

Optimal design of hierarchically structured nanoporous catalysts

The stellar progress in the capabilities to synthesize nanostructured materials prompts for the following questions: What are the optimal nanoscopic environment and the optimal pore network for a given heterogeneous catalytic process? Catalyst structure involves the active sites, but also the immediate geometric environment, as well as the pore network linking these sites to the macroscopic world, allowing reactant molecules to access and products to leave the sites. Diffusion limitations may lead to considerable loss in activities and selectivities There now exist many techniques to synthesize uniform pore sizes and pore networks. While beautifully crafted, the final pore architectures are empirical and not resulting from any optimization study. On the other hand, for years, theoreticians have studied diffusion and reaction problems in pore networks, at times when pore networks could not be designed to the accuracy we are capable of today. This paper aims to draw the attention of experimentalists to the opportunities that textural optimization studies provide to rationally instead of empirically design hierarchically structured porous catalysts.