Fractal analysis of concurrently prepared latex rubber casts of the bronchial and vascular systems of the human lung

Fractal geometry (FG) is a branch of mathematics that instructively characterizes structural complexity. Branched structures are ubiquitous in both the physical and the biological realms. Fractility has therefore been termed nature's design. The fractal properties of the bronchial (airway) system, the pulmonary artery and the pulmonary vein of the human lung generates large respiratory surface area that is crammed in the lung. Also, it permits the inhaled air to intimately approximate the pulmonary capillary blood across a very thin blood–gas barrier through which gas exchange to occur by diffusion. Here, the bronchial (airway) and vascular systems were simultaneously cast with latex rubber. After corrosion, the bronchial and vascular system casts were physically separated and cleared to expose the branches. The morphogenetic (Weibel's) ordering method was used to categorize the branches on which the diameters and the lengths, as well as the angles of bifurcation, were measured. The fractal dimensions ( D F ) were determined by plotting the total branch measurements against the mean branch diameters on double logarithmic coordinates (axes). The diameter-determined D F values were 2.714 for the bronchial system, 2.882 for the pulmonary artery and 2.334 for the pulmonary vein while the respective values from lengths were 3.098, 3.916 and 4.041. The diameters yielded D F values that were consistent with the properties of fractal structures (i.e. self-similarity and space-filling). The data obtained here compellingly suggest that the design of the bronchial system, the pulmonary artery and the pulmonary vein of the human lung functionally comply with the Hess–Murray law or ‘the principle of minimum work’.

The supine position improves but does not normalize the blunted pulmonary capillary blood volume response to exercise in mild COPD

Patients with mild chronic obstructive pulmonary disease (COPD) demonstrate resting pulmonary vascular dysfunction as well as a blunted pulmonary diffusing capacity (DLCO) and pulmonary capillary blood volume (VC) response to exercise. The transition from the upright to supine position increases central blood volume and perfusion pressure, which may overcome microvascular dysfunction in an otherwise intact alveolar-capillary interface. The present study examined whether the supine position normalized DLCO and VC responses to exercise in mild COPD. Sixteen mild COPD participants and 13 age-, gender-, and height-matched controls completed DLCO maneuvers at rest and during exercise in the upright and supine position. The multiple [Formula: see text]-DLCO method was used to determine DLCO, VC, and membrane diffusion capacity (DM). All three variables were adjusted for alveolar volume (DLCOAdj, VCAdj, and DMAdj). The supine position reduced alveolar volume similarly in both groups, but oxygen consumption and cardiac output were unaffected. DLCOAdj, DMAdj, and VCAdj were all lower in COPD. These same variables all increased with upright and supine exercise in both groups. DLCOAdj was unaffected by the supine position. VCAdj increased in the supine position similarly in both groups. DMAdj was reduced in the supine position in both groups. While the supine position increased exercise VCAdj in COPD, the increase was of similar magnitude to healthy controls; therefore, exercise VC remained blunted in COPD. The persistent reduction in exercise DLCO and VC when supine suggests that pulmonary vascular destruction is a contributing factor to the blunted DLCO and VC response to exercise in mild COPD. NEW & NOTEWORTHY Patients with mild chronic obstructive pulmonary disease demonstrate a combination of reversible pulmonary microvascular dysfunction and irreversible pulmonary microvascular destruction.

Differences in alveolo-capillary equilibration in healthy subjects on facing O2 demand

Oxygen diffusion across the air-blood barrier in the lung is commensurate with metabolic needs and ideally allows full equilibration between alveolar and blood partial oxygen pressures. We estimated the alveolo-capillary O2 equilibration in 18 healthy subjects at sea level at rest and after exposure to increased O2 demand, including work at sea level and on hypobaric hypoxia exposure at 3840 m (PA ~ 50 mmHg). For each subject we estimated O2 diffusion capacity (DO2), pulmonary capillary blood volume (Vc) and cardiac output ($$\dot{Q}$$Q̇). We derived blood capillary transit time $${\boldsymbol{(}}{\boldsymbol{T}}{\boldsymbol{t}}{\boldsymbol{=}}\frac{{\boldsymbol{V}}{\boldsymbol{c}}}{\dot{{\boldsymbol{Q}}}}{\boldsymbol{)}}$$(Tt=VcQ̇) and the time constant of the equilibration process ($${\boldsymbol{\tau }}{\boldsymbol{=}}\frac{{\boldsymbol{\beta }}{\boldsymbol{V}}{\boldsymbol{c}}}{{\boldsymbol{D}}{{\boldsymbol{O}}}_{{\boldsymbol{2}}}}$$τ=βVcDO2, β being the slope of the hemoglobin dissociation curve). O2 equilibration at the arterial end of the pulmonary capillary was defined as $${{\bf{L}}}_{{\bf{e}}{\bf{q}}}{\boldsymbol{=}}{{\bf{e}}}^{{\boldsymbol{-}}\frac{{\bf{T}}t}{{\boldsymbol{\tau }}}}$$Leq=e−Ttτ. Leq greately differed among subjects in the most demanding O2 condition (work in hypoxia): lack of full equilibration was found to range from 5 to 42% of the alveolo-capillary PO2 gradient at the venous end. The present analysis proves to be sensible enough to highlight inter-individual differences in alveolo-capillary equilibration among healthy subjects.

Gas Exchange

Gas Exchange explains how four processes—delivery of oxygen, excretion of carbon dioxide, matching of ventilation and perfusion, and diffusion—allow the respiratory system to maintain normal partial pressures of oxygen (PaO2) and carbon dioxide (PaCO2) in the arterial blood. Partial pressure is important because O2 and CO2 molecules diffuse between alveolar gas and pulmonary capillary blood and between systemic capillary blood and the tissues along their partial pressure gradients, and diffusion continues until the partial pressures are equal. Ventilation is an essential part of gas exchange because it delivers O2, eliminates CO2, and determines ventilation–perfusion ratios. This chapter also explains how and why abnormalities in each of these processes may reduce PaO2, increase PaCO2, or both.