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244 Reverse Engineering – Recent Advances and Applications 2 Will-be-set-by-IN-TECH Fig. 1. Scanning electron micrograph of the perfusion-fixed lung tissue (Weibel, 1984), showing transition between peripheral bronchiole (BL) and terminal bronchiole (T). Alveolar ducts are denoted by arrows in the direction of downstream flow, near pulmonary arteries (A) and veins (V). Scale marker is 200 μm. in how they treat the exchange-surface, they all consistently predict a region of the parameter space in which the current is “robust;” i.e. changes or error in the parameters do not affect the functional state of the system. Finally, we apply physiological data for the human lung–the prototypical mammalian lung studied here–to validate these models against experimental measurements; we use them as a tool to reverse-engineer how the human lung supplies the body with increasing oxygen currents under the body’s increasing oxygen demands that occur, for example, during heavy exercise. 2. Motivation Mammalian lungs regulate the exchange of respiratory gases (here we focus on molecular oxygen, O2) between air and pulmonary blood, delivering oxygen to cells that use it to drive energy metabolism, such as glycolysis. Beginning from the trachea, these gases are transported downstream throughout the bronchial tree by convection until their speed drops drops below the local diffusion speed, wherein further transport toward the periphery of the lung occurs by stationary diffusion. As shown in Fig. 1, the airways in which this transition occurs, termed the transitional bronchioles, are defined by the appearance of air sacs, or alveoli, that appear along the walls of the airway channels, termed acinar ducts (Weibel, 1984). While only sparsely populating the walls of the transitional bronchioles, these alveoli dominate the walls of the acinar airways, which lay only a few branch generations downstream of the transitional bronchioles. The epithelial cells lining the alveoli are tightly packed, so they form a jointless surface of alveolar membranes across which the gas exchange almost entirely occurs (Weibel, 1984). The oxygen uptake rate, I, measured in units of moles of gas transferred across the entire surface of alveolar membranes of the lung per unit time, measures the ability of the body to
Reverse-Engineering the Robustness of Mammalian Lungs Reverse-Engineering the Robustness of Mammalian Lungs 3 meet the changing energetic demands of its tissues under changing physiological conditions, such as foraging or predation. For example, altering cell metabolism increases/decreases oxygen demands (as a vital component in glycolysis), and the mammalian lung, as a whole, responds by automatically increasing/decreasing this current without invoking any biochemical feedback loops. There are several steps between oxygen in the air and its final delivery to the cell. The rate-limiting step is its diffusion to, and across, the surface of alveolar membranes that collectively serve as the gas-exchange surface. It then binds with the erythrocytes, or red blood cells in the pulmonary arteries, to any of the four binding sites on hemoglobin, which allows for its dissolution in blood plasma. An oxygen partial pressure difference between air, pa, and erythrocytes, pe, serves as the driving force in the oxygen uptake rate across the membranes, and can be written as (Comroe, 1962; Weibel, 1984): I = T lung (pa − pe) , (1) wherein T lung is the total diffusing capacity of the mammalian lung (in units of oxygen molecules transferred to erythrocyte per unit time and pressure). Because diffusing oxygen moves first across a barrier of alveolar membranes and then through the blood plasma, they can be viewed as resistors connected in series (Hou et al., 2010), in which the same current flows through each biological “resistor.” Equation 1 can then be rewritten in terms of only the oxygen partial pressure difference across the membranes alone, pa − p b (Weibel, 1984): wherein Tm is the membrane’s diffusing capacity for oxygen. I = Tm (pa − p b) , (2) As the body increasingly demands more oxygen to supply muscles and other tissues with chemical energy, the uptake rate, as given by Eqn. 2, increases 20-fold under the most strenuous exercise and breathing conditions as compared to the resting state, although the driver of the oxygen current–the partial pressure difference–increases only 2–fold under these same conditions (Weibel, 1992). The diffusing capacity of the membranes is, Tm, therefore, is almost entirely responsible for this increase in oxygen uptake rate; not the partial pressure difference. To put this result in perspective, consider an analogy between electrical and biological circuits, wherein biological surface areas and permeabilities play the role of electrical impedance, chemical/nutrient exchange and uptake rates across these biological surfaces (e.g. oxygen uptake rates) play the role of electric currents, and partial pressure differences across biological surfaces play the role of voltage differences across electrical components. Relationships of the type given by Eqn. 2 are therefore analogous to Ohm’s law in electric circuits. To say that the oxygen partial pressure difference does not, in effect, provide for the entirety of the observed increase in oxygen current supplied to the body by the lung, is equivalent to stating that a voltage difference is not entirely responsible for increasing the electrical current through a circuit’s component, such as a resistor. Here we use mathematical modeling to explain this phenomenon, and use it to determine the cause of the lung’s robustness–it’s ability to provide a constant oxygen current to the blood despite disease or damage to its exchange tissues. 245
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REVERSE ENGINEERING - RECENT ADVANC
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Contents Preface IX Part 1 Software
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Preface Introduction In the recent
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Preface XI and con’s related to t
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Preface XIII the step-by-step appli
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Part 1 Software Reverse Engineering
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4 Reverse Engineering - Recent Adva
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10 Reverse Engineering - Recent Adv
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62 Fig. 1. Model, metamodels and tr
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108 Table 1. Number of smoothers an
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1. Introduction 60 Surface Reconstr
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Surface Reconstruction from Unorgan
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1. Introduction A Systematic Approa
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A Systematic Approach for Geometric
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A Review on Shape Engineering and D
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Integrating Reverse Engineering and
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