Branching design of the bronchial tree based on a diameter-flow relationship

Kitaoka, Hiroko, and Béla Suki. Branching designof the bronchial tree based on a diameter-flow relationship.J. Appl. Physiol. 82(3): 968-976, 1997.We propose a method for designing the bronchial tree where thebranching process is stochastic and the diameter(d) of a branch is determined by itsflow rate (Q). We use two principles: the continuumequation for flow division and a power-law relationship betweend and Q, given by Q ~ dⁿ,where n is the diameter exponent. The value ofn has been suggested to be ~3. Weassume that flow is divided iteratively with a random variable for theflow-division ratio, defined as the ratio of flow in the branch to thatin its parent branch. We show that the cumulative probabilitydistribution function of Q, P(>Q) is proportional to Q¹. Weanalyzed prior morphometric airway data (O. G. Raabe, H. C. Yeh, H. M. Schum, and R. F. Phalen, Report No.LF-53, 1976) and found that the cumulative probabilitydistribution function of diameters, P(>d), isproportional to dⁿ, which supportsthe validity of Q ~ dⁿ sinceP(>Q) ~ Q¹. This allowed us toassign diameters to the segments of the flow-branching pattern. Wemodeled the bronchial trees of four mammals and found that theirstatistical features were in good accordance with the morphometricdata. We conclude that our design method is appropriate for robustgeneration of bronchial tree models.

     

Dynamic properties of lung parenchyma: mechanical contributions of fiber network and interstitial cells

Yuan, Huichin, Edward P. Ingenito, and Béla Suki.Dynamic properties of lung parenchyma: mechanical contributions offiber network and interstitial cells. J. Appl.Physiol. 83(5): 1420-1431, 1997.We investigatedthe contributions of the connective tissue fiber network andinterstitial cells to parenchymal mechanics in a surfactant-freesystem. In eight strips of uniform dimension from guinea pig lung, weassessed the storage (G) and loss (G") moduli by usingpseudorandom length oscillations containing a specially designed set ofseven frequencies from 0.07 to 2.4 Hz at baseline, during methacholine(MCh) challenge, and after death of the interstitial cells.Measurements were made at mean forces of 0.5 and 1 g and strainamplitudes of 5, 10, and 15% and were repeated 12 h later in the same,but nonviable samples. The results were interpreted using a linearviscoelastic model incorporating both tissue damping (G) and stiffness(H). The G and G" increased linearly with the logarithmof frequency, and both G and H showed negative strain amplitude andpositive mean force dependence. After MCh challenge, the G andG" spectra were elevated uniformly, and G and H increased by<15%. Tissue stiffness, strain amplitude, and mean force dependencewere virtually identical in the viable and nonviable samples. The G andhence energy dissipation were ~10% smaller in the nonviable samplesdue to absence of actin-myosin cross-bridge cycling. We conclude thatthe connective tissue network may also dominate parenchymal mechanicsin the intact lung, which can be influenced by the tone or contractionof interstitial cells.

     

Nonlinearity and harmonic distortion of dog lungs measured by low-frequency forced oscillations

The nonlinearity of lung tissues and airways was studied in six anesthetized and paralyzed open-chest dogs by means of 0.1-Hz sinusoidal volume forcing at mean transpulmonary pressures (Ptp) of 5 and 10 cmH2O. Lung resistance (RL) and elastance (EL) were determined in a 32-fold range (15-460 ml) of tidal volume (VT), both by means of spectrum analysis at the fundamental frequency and with conventional time-domain techniques. Alveolar capsules were used to separate the tissue and airway properties. A very small amplitude dependence was found: with increasing VT, the frequency-domain estimates of RL decreased by 5.3 and 14%, whereas EL decreased by 20 and 22% at Ptp = 5 and 10 cmH2O, respectively. The VT dependences of the time-domain estimates of RL were higher: 10.5 and 20% at Ptp = 5 and 10 cmH2O, respectively, whereas EL remained the same. The airway resistance increased moderately with flow amplitude and was smaller at the higher Ptp level. Analysis of the harmonic distortions of airway opening pressure and the alveolar pressures indicated that nonlinear harmonic production is moderate even at the highest VT and that VT dependence is homogeneous throughout the tissues. In three other dogs it was demonstrated that VT dependences of RL and EL were similar in situ and in isolated lungs at both Ptp levels.     

Mechanical interactions between collagen and proteoglycans: implications for the stability of lung tissue.

Collagen and elastin are thought to dominate the elasticity of the connective tissue including lung parenchyma. The glycosaminoglycans on the proteoglycans may also play a role because osmolarity of interstitial fluid can alter the repulsive forces on the negatively charged glycosaminoglycans, allowing them to collapse or inflate, which can affect the stretching and folding pattern of the fibers. Hence, we hypothesized that the elasticity of lung tissue arises primarily from 1) the topology of the collagen-elastin network and 2) the mechanical interaction between proteoglycans and fibers. We measured the quasi-static, uniaxial stress-strain curves of lung tissue sheets in hypotonic, normal, and hypertonic solutions. We found that the stress-strain curve was sensitive to osmolarity, but this sensitivity decreased after proteoglycan digestion. Images of immunofluorescently labeled collagen networks showed that the fibers follow the alveolar walls that form a hexagonal-like structure. Despite the large heterogeneity, the aspect ratio of the hexagons at 30% uniaxial strain increased linearly with osmolarity. We developed a two-dimensional hexagonal network model of the alveolar structure incorporating the mechanical properties of the collagen-elastin fibers and their interaction with proteoglycans. The model accounted for the stress-strain curves observed under all experimental conditions. The model also predicted how aspect ratio changed with osmolarity and strain, which allowed us to estimate the Young's modulus of a single alveolar wall and a collagen fiber. We therefore identify a novel and important role for the proteoglycans: they stabilize the collagen-elastin network of connective tissues and contribute to lung elasticity and alveolar stability at low to medium lung volumes.     

Tissue heterogeneity in the mouse lung: effects of elastase treatment.

We developed a network model in an attempt to characterize heterogeneity of tissue elasticity of the lung. The model includes a parallel set of pathways, each consisting of an airway resistance, an airway inertance, and a tissue element connected in series. The airway resistance, airway inertance, and the hysteresivity of the tissue elements were the same in each pathway, whereas the tissue elastance (H) followed a hyperbolic distribution between a minimum and maximum. To test the model, we measured the input impedance of the respiratory system of ventilated normal and emphysematous C57BL/6 mice in closed chest condition at four levels of positive end-expiratory pressures. Mild emphysema was developed by nebulized porcine pancreatic elastase (PPE) (30 IU/day x 6 days). Respiratory mechanics were studied 3 wk following the initial treatment. The model significantly improved the fitting error compared with a single-compartment model. The PPE treatment was associated with an increase in mean alveolar diameter and a decrease in minimum, maximum, and mean H. The coefficient of variation of H was significantly larger in emphysema (40%) than that in control (32%). These results indicate that PPE treatment resulted in increased time-constant inequalities associated with a wider distribution of H. The heterogeneity of alveolar size (diameters and area) was also larger in emphysema, suggesting that the model-based tissue elastance heterogeneity may reflect the underlying heterogeneity of the alveolar structure.     

Differential effects of static and cyclic stretching during elastase digestion on the mechanical properties of extracellular matrices.

Enzyme activity plays an essential role in many physiological processes and diseases such as pulmonary emphysema. While the lung is constantly exposed to cyclic stretching, the effects of stretch on the mechanical properties of the extracellular matrix (ECM) during digestion have not been determined. We measured the mechanical and failure properties of elastin-rich ECM sheets loaded with static or cyclic uniaxial stretch (40% peak strain) during elastase digestion. Quasistatic stress-strain measurements were taken during 30 min of digestion. The incremental stiffness of the sheets decreased exponentially with time during digestion. However, digestion in the presence of static stretch resulted in an accelerated stiffness decrease, with a time constant that was nearly 3 x smaller (7.1 min) than during digestion alone (18.4 min). These results were supported by simulations that used a nonlinear spring network model. The reduction in stiffness was larger during static than cyclic stretch, and the latter also depended on the frequency. Stretching at 20 cycles/min decreased stiffness less than stretching at 5 cycles/min, suggesting a rate-dependent coupling between mechanical forces and enzyme activity. Furthermore, pure digestion reduced the failure stress of the sheets from 88 +/- 21 kPa in control to 29 +/- 15 kPa (P < 0.05), while static and cyclic stretch resulted in a failure stress of 7 +/- 5 kPa (P < 0.05). We conclude that not only the presence but the dynamic nature of mechanical forces have a significant impact on enzyme activity, hence the deterioration of the functional properties of the ECM during exposure to enzymes.     

Electromuscular incapacitation results from stimulation of spinal reflexes

Electronic stun devices (ESD) often used in law enforcement, military action or self defense can induce total body uncoordinated muscular activity, also known as electromuscular incapacitation (EMI). During EMI the subject is unable to perform purposeful or coordinated movements. The mechanism of EMI induction has not been reported, but has been generally thought to be direct muscle and nerve excitation from the fields generated by ESDs. To determine the neuromuscular mechanisms linking ESD to induction of EMI, we investigated EMI responses using an anesthetized pig model. We found that EMI responses to ESD application can best be simulated by simultaneous stimulation of motor and sensory peripheral nerves. We also found that application of local anesthetics limited the response of ESD to local muscle stimulation and abolished the total body EMI response. Stimulation of the pure sensory peripheral nerves or nerves that are primarily motor nerves induced muscle responses that are consistent with well defined spinal reflexes. These findings suggest that the mechanism of ESD‐induced EMI is mediated by excitation of multiple simultaneous spinal reflexes. Although direct motor‐neuron stimulation in the region of ESD contact may significantly add to motor reactions from ESD stimulation, multiple spinal reflexes appear to be a major, and probably the dominant mechanism in observed motor response. Bioelectromagnetics 30:411–421, 2009. © 2009 Wiley‐Liss, Inc.