A non-linear theory of the distribution of pulmonary ventilation

Assessment Of Changes In Regional Xenon-Ventilation, Perfusion, And Ventilation-Perfusion Mismatch Using Dual-Energy Computed Tomography After Pharmacological Treatment In Patients With Chronic Obstructive Pulmonary Disease: Visual And Quantitative Analysis

Purpose

To assess changes in regional ventilation (V), perfusion (Q), and V-Q mismatch in patients with chronic obstructive pulmonary disease (COPD) after pharmacologic treatment using combined xenon-enhanced V and iodine-enhanced Q dual-energy CT (DECT).

Patients and methods

Combined V and Q DECT were performed at baseline and after three-month pharmacologic treatment in 52 COPD patients. Anatomically co-registered virtual non-contrast images, V, Q, and V/Q_ratio maps were obtained. V/Q pattern was visually determined to be matched, mismatched, or reversed-mismatched and compared with the regional parenchymal disease patterns of each segment. DECT parameters for V, Q, and V-Q imbalance were quantified.

Results

The parenchymal patterns on CT were not changed at follow-up. The segments with matched V/Q pattern were increased (80.2% to 83.6%) as the segments with reversed-mismatched V/Q pattern were decreased with improving ventilation (17.6% to 13.8%) after treatment. Changes of V/Q patterns were mostly observed in segments with bronchial wall thickening. Compared with patients without bronchial wall thickening, the quantified DECT parameters of V-Q imbalance were significantly improved in patients with bronchial wall thickening (p < 0.05). Changes in forced expiratory volume in one second after treatment were correlated with changes in the quantified DECT parameters (r = 0.327–0.342 or r = −0.406 and −0.303; p < 0.05).

Conclusion

DECT analysis showed that the V-Q imbalance was improved after the pharmacological treatment in COPD patients, although the parenchymal disease patterns remained unchanged. This improvement of V-Q imbalance may occur mostly in the areas with bronchial wall thickening.

Contributions of Kinetic Energy and Viscous Dissipation to Airway Resistance in Pulmonary Inspiratory and Expiratory Airflows in Successive Symmetric Airway Models With Various Bifurcation Angles

The aim of this study was to investigate and quantify contributions of kinetic energy and viscous dissipation to airway resistance during inspiration and expiration at various flow rates in airway models of different bifurcation angles. We employed symmetric airway models up to the 20th generation with the following five different bifurcation angles at a tracheal flow rate of 20 L/min: 15 deg, 25 deg, 35 deg, 45 deg, and 55 deg. Thus, a total of ten computational fluid dynamics (CFD) simulations for both inspiration and expiration were conducted. Furthermore, we performed additional four simulations with tracheal flow rate values of 10 and 40 L/min for a bifurcation angle of 35 deg to study the effect of flow rate on inspiration and expiration. Using an energy balance equation, we quantified contributions of the pressure drop associated with kinetic energy and viscous dissipation. Kinetic energy was found to be a key variable that explained the differences in airway resistance on inspiration and expiration. The total pressure drop and airway resistance were larger during expiration than inspiration, whereas wall shear stress and viscous dissipation were larger during inspiration than expiration. The dimensional analysis demonstrated that the coefficients of kinetic energy and viscous dissipation were strongly correlated with generation number. In addition, the viscous dissipation coefficient was significantly correlated with bifurcation angle and tracheal flow rate. We performed multiple linear regressions to determine the coefficients of kinetic energy and viscous dissipation, which could be utilized to better estimate the pressure drop in broader ranges of successive bifurcation structures.

An object-oriented model of the cardiopulmonary system with emphasis on the gravity effect

We introduce a novel comprehensive model of the cardiopulmonary system with emphasis on perfusion and ventilation distribution along the vertical thorax axis under the gravity effect. By using an object-oriented environment, the complex physiological system can be represented by a network of electrical, lumped-element compartments. The lungs are divided into three zones: upper, middle, and lower zone. Blood flow increases with the distance from the apex to the base of the lungs. The upper zone is characterized by a complete collapse of the pulmonary capillary vasculature; thus, there is no flow in this zone. The second zone has a "waterfall effect" where the blood flow is determined by the difference between the pulmonary-arterial and alveolar pressures. At resting position, the upper lobes of the lungs are more expanded than the middle and lower lobes. However, during spontaneous breathing, ventilation is nonuniform with more air entering the lower lobes than the middle and upper lobes. A simulative model of the complete system is developed which shows results in good agreement with the literature.

Human Physiology in an Aquatic Environment

Water covers over 70% of the earth, has varying depths and temperatures and contains much of the earth's resources. Head-out water immersion (HOWI) or submersion at various depths (diving) in water of thermoneutral (TN) temperature elicits profound cardiorespiratory, endocrine, and renal responses. The translocation of blood into the thorax and elevation of plasma volume by autotransfusion of fluid from cells to the vascular compartment lead to increased cardiac stroke volume and output and there is a hyperperfusion of some tissues. Pulmonary artery and capillary hydrostatic pressures increase causing a decline in vital capacity with the potential for pulmonary edema. Atrial stretch and increased arterial pressure cause reflex autonomic responses which result in endocrine changes that return plasma volume and arterial pressure to preimmersion levels. Plasma volume is regulated via a reflex diuresis and natriuresis. Hydrostatic pressure also leads to elastic loading of the chest, increasing work of breathing, energy cost, and thus blood flow to respiratory muscles. Decreases in water temperature in HOWI do not affect the cardiac output compared to TN; however, they influence heart rate and the distribution of muscle and fat blood flow. The reduced muscle blood flow results in a reduced maximal oxygen consumption. The properties of water determine the mechanical load and the physiological responses during exercise in water (e.g. swimming and water based activities). Increased hydrostatic pressure caused by submersion does not affect stroke volume; however, progressive bradycardia decreases cardiac output. During submersion, compressed gas must be breathed which introduces the potential for oxygen toxicity, narcosis due to nitrogen, and tissue and vascular gas bubbles during decompression and after may cause pain in joints and the nervous system.

The ventilation distribution of helium-oxygen mixtures and the role of inertial losses in the presence of heterogeneous airway obstructions

The regional distribution of inhaled gas within the lung is affected in part by normal variations in airway geometry or by obstructions resulting from disease. In the present work, the effects of heterogeneous airway obstructions on the distribution of air and helium-oxygen were examined using an in vitro model, the two compartments of a dual adult test lung. Breathing helium-oxygen resulted in a consistently more uniform distribution, with the gas volume delivered to a severely obstructed compartment increased by almost 80%. An engineering approach to pipe flow was used to analyze the test lung and was extrapolated to a human lung model to show that the in vitro experimental parameters are relevant to the observed in vivo conditions. The engineering analysis also showed that helium-oxygen can decrease the relative weight of the flow resistance due to obstructions if they are inertial in nature (i.e., density dependent) due to either turbulence or laminar convective losses.

Pulmonary gas exchange in diving

Diving-related pulmonary effects are due mostly to increased gas density, immersion-related increase in pulmonary blood volume, and (usually) a higher inspired Po2. Higher gas density produces an increase in airways resistance and work of breathing, and a reduced maximum breathing capacity. An additional mechanical load is due to immersion, which can impose a static transrespiratory pressure load as well as a decrease in pulmonary compliance. The combination of resistive and elastic loads is largely responsible for the reduction in ventilation during underwater exercise. Additionally, there is a density-related increase in dead space/tidal volume ratio (Vd/Vt), possibly due to impairment of intrapulmonary gas phase diffusion and distribution of ventilation. The net result of relative hypoventilation and increased Vd/Vt is hypercapnia. The effect of high inspired Po2and inert gas narcosis on respiratory drive appear to be minimal. Exchange of oxygen by the lung is not impaired, at least up to a gas density of 25 g/l. There are few effects of pressure per se, other than a reduction in the P50 of hemoglobin, probably due to either a conformational change or an effect of inert gas binding.

A Modeling Study of the Effect of Gravity on Airflow Distribution and Particle Deposition in the Lung

Inhalation of particles generated as a result of thermal degradation from fire or smoke, as may occur on spacecraft, is of major health concern to space-faring countries. Knowledge of lung airflow and particle transport under different gravity environments is required to addresses this concern by providing information on particle deposition. Gravity affects deposition of particles in the lung in two ways. First, the airflow distribution among airways is changed in different gravity environments. Second, particle losses by sedimentation are enhanced with increasing gravity. In this study, a model of airflow distribution in the lung that accounts for the influence of gravity was used for a mathematical description of particle deposition in the human lung to calculate lobar, regional, and local deposition of particles in different gravity environments. The lung geometry used in the mathematical model contained five lobes that allowed the assessment of lobar ventilation distribution and variation of particle deposition. At zero gravity, it was predicted that all lobes of the lung expanded and contracted uniformly, independent of body position. Increased gravity in the upright position increased the expansion of the upper lobes and decreased expansion of the lower lobes. Despite a slight increase in predicted deposition of ultrafine particles in the upper lobes with decreasing gravity, deposition of ultrafine particles was generally predicted to be unaffected by gravity. Increased gravity increased predicted deposition of fine and coarse particles in the tracheobronchial region, but that led to a reduction or even elimination of deposition in the alveolar region for coarse particles. The results from this study show that existing mathematical models of particle deposition at 1 G can be extended to different gravity environments by simply correcting for a gravity constant. Controlled studies in astronauts on future space missions are needed to validate these predictions.

Airflow distribution in the human lung and its influence on particle deposition

Realistic descriptions of lung geometry and physiology are the primary determinants of accurate predictions of inhaled particle deposition and distribution in the human lung. While there have been considerable efforts devoted to geometry reconstruction, little attention has been given to lung ventilation as applied to particle deposition applications. Models of lung ventilation based on pressure differential between extrathoracic airways and the pleural cavity were developed and used to calculate lobar and regional deposition of particles in the human lung. Local airflow in the lung varied in accordance with regional physiological properties. Calculations showed that airflow rate entering each lobe was different for compliant and noncompliant lung models and similar for uniform and nonuniform lung expansions. Regional particle deposition predictions were almost identical between the two compliance models. However, differences in lobar depositions were observed. The coupled lung ventilation and deposition models can be used in site-specific deposition predictions of inhaled particles in the human lungs.

Distribution of blood flow and ventilation in the lung: gravity is not the only factor

Current textbooks in anaesthesia describe how gravity affects the regional distribution of ventilation and blood flow in the lung, in terms of vertical gradients of pleural pressure and pulmonary vascular pressures. This concept fails to explain some of the clinical features of disturbed lung function. Evidence now suggests that gravity has a less important role in the variation of regional distribution than structural features of the airways and blood vessels. We review more recent studies that used a variety of methods: external radioactive counters, measurements using inhaled and injected particles, and computer tomography scans. These give a higher spatial resolution of regional blood flow and ventilation. The matching between ventilation and blood flow in these small units of lung is considered; the effects of microgravity, increased gravity, and different postures are reviewed, and the application of these findings to conditions such as acute lung injury is discussed. Down to the scale of the acinus, there is considerable heterogeneity in the distribution of both ventilation and blood flow. However, the matching of blood flow with ventilation is well maintained and may result from a common pattern of asymmetric branching of the airways and blood vessels. Disruption of this pattern may explain impaired gas exchange after acute lung injury and explain how the prone position improves gas exchange.

Effects of viscoelasticity on volume distribution in a two-compartmental model of normal and sick lungs

Among the models describing respiratory mechanics none has been published with the characteristics of two lung compartments including the viscoelastic properties. We used such a model to describe the inspiratory compartmental volume distribution under homogeneous and inhomogeneous conditions. The present mathematical model was tested against actual data and proven accurate. The volume distribution was studied using data from normal subjects and from patients with COPD and ARDS. In a normal lung, changes in viscoelastic constants in one compartment can modify substantially the volume distribution diverting more or less gas to the other compartment. In diseased compartments, the increase of viscoelasticity increased the difference between the compartments and the opposite was true in the less affected compartment. In conclusion, the viscoelastic properties are of paramount importance in determining gas distribution in normal and sick lungs.

Regional ventilation in statically and dynamically hyperinflated dogs

Using the parenchymal marker technique in normal anesthetized dogs, we compared the dynamics of regional lung expansion between two ventilation strategies designed to increase mean thoracic volume. Dynamic hyperinflation (DH was produced by ventilating the lungs at a rate of 50 breaths/min and with a duty cycle of 0.5. Static hyperinflation (SH) was produced through the application of extrinsic positive end-expiratory pressure while the lungs were ventilated at a rate of 15 breaths/min and with a duty cycle of 0.15. Regional tidal volume (VT,r), regional functional residual volume, and the time delay between regional expansion and the flow signal at the common airway were computed for up to 100 regions/lobe in 5 animals. Ventilation strategy had no effect on the overall variance of VT,r within lobes. Although the VT,r measured during SH correlated with VT,r measured during DH, the average correlation coefficient was only 0.69. Ventilation rate-related differences in VT,r and regional functional residual capacity varied with the regional time delay in ways qualitatively consistent with parallel inhomogeneity of unit time constants. However, a large component of frequency-dependent behavior remains unexplained by established mechanisms. We conclude that DH and SH should not be considered equivalent lung unit recruitment strategies.

Implications of a biphasic two-compartment model of constant flow ventilation for the clinical setting

PURPOSE

To investigate the theoretical effects of changing frequency (f), duty cycle (D), or end-inspiratory pause length on the distribution of ventilation and compartmental pressure in a heterogeneous, two compartment pulmonary model inflated by constant flow.

METHODS

Differential equations governing compartmental volume changes were derived and solved. Validation was conducted in a mechanical lung analogue with two mechanically independent compartments. Model predictions were then generated over wide ranges of f, D, or end-inspiratory pause.

RESULTS

Disparity of compartmental end-expiratory pressure was identified as the primary mechanism by which changes in f, D, or pause alter the distribution of ventilation. Distribution of peak pressures was less sensitive to such changes. Compartmental ventilation was much less uniform than compartmental peak pressure. Ventilation could not be made entirely uniform by changes of f, D, or pause within the usual clinical range.

CONCLUSIONS

In a linear, two compartment model of the respiratory system, disparity of compartmental end-expiratory pressures is the primary mechanism by which changes of f, D, or pause alter the distribution of ventilation during inflation with constant flow. Ventilation is less evenly distributed than peak alveolar pressure, and there are limits to the beneficial effects on the distribution of ventilation to be gained from manipulations of machine settings.

Factors affecting distribution of airflow in a human tracheobronchial cast

Air velocity was measured at end airways of hollow replicate casts of the human tracheobronchial tree in order to determine the flow distribution within casts extending to 3 mm diameter airways. Measurements were made by hot-wire anemometry for constant inspiratory flow rates of 7.5, 15, 30 and 60 L.min-1. Average flow distribution among the lung lobes was as follows: right upper, 18.5%; right middle, 9.2%; right lower, 32.3%; left upper, 15.7%; and left lower, 24.3%. An empirical model derived from the experimental flow distribution data demonstrated the effect of various morphometric parameters of the hollow cast on the distribution of airflow. Airway cross-sectional area, branching angle and total path-length were found to have the greatest influence. As the tracheal flow rate decreased from 60 to 7.5 L.min-1, the influence of branching angle was reduced, while total path-length became more influential. These results provide evidence for the transition of flow regimes within the TB tree within normal physiological flow ranges.

Flow distribution in a single bifurcation during high-frequency oscillation

The distribution of flow in a single bifurcation was studied to examine what factors played a critical role. Flow was preferentially directed down the straightest pathway when higher frequencies and/or larger tidal volumes were used, but otherwise followed the pattern dictated by the distal impedance regardless of bifurcation geometry. In a symmetrical model, the observed flow distribution was in good agreement with a mathematical prediction based on linear impedance theory, though this was not the case when tidal volumes were increased. The difference in mean pressure between the two terminal units was also a strong function of branching angle and the Reynolds number. These findings suggest that the geometrical factors and local flow conditions contribute to both the flow and mean pressure distribution in an inertia-induced nonlinear manner. Consequently, linear impedance theory can be applied only to the limited situation of low tidal volume and symmetric configuration.

Regional alveolar pressure during periodic flow. Dual manifestations of gas inertia

We measured pressure excursions at the airway opening and at the alveoli (PA) as well as measured the regional distribution of PA during forced oscillations of six excised dog lungs while frequency (f[2-32 Hz]), tidal volume (VT [5-80 ml]), and mean transpulmonary pressure (PL [25, 10, and 6 cm H2O]) were varied. PA's were measured in four alveolar capsules glued to the pleura of different lobes. The apex-to-base ratio of PA's was used as an index of the distribution of dynamic lung distension. At low f, there was slight preferential distension of the lung base which was independent of VT, but at higher f, preferential distension of the lung apex was found when VT's were small, whereas preferential distension of the lung base was found when VT's approached or exceeded dead space. These VT-related changes in distribution at high frequencies seem to depend upon the branching geometry of the central airways and the relative importance of convective momentum flux vs. unsteady inertia of gas residing therein, which, in this study, we showed to be proportional to the ratio VT/VD*, where VD* is an index of dead space. Furthermore, they imply substantial alteration in the distribution of ventilation during high frequency ventilation as f, VT, and PL vary. The data also indicate that alveolar and airway opening pressure costs per unit flow delivered at the airway opening exhibit weakly nonlinear behavior and that resonant amplification of PA's, which has been described previously for the case of very small VT's, persists but is damped as VT's approach dead space values.

Effect of posture on inter-regional distribution of pulmonary ventilation in man

Regional ventilation per unit alveolar volume (V/VA) and regional lung expansion (FRCR/TLCR) were measured in twelve normal male human subjects in seated, supine, lateral decubitus and prone postures using a gamma camera and inhalation of the radioactive gases 81Krm (half-life 13 sec) and 85Krm (half-life 4.4 h). FRCR/TLCR decreased from superior to inferior in all postures except prone where it was uniform; V/VA increased from superior to inferior except in the prone position where it was uniform. In the horizontal axis FRCR/TLCR and V/VA were uniformly distributed except for cranial to caudal gradients (with lower values caudally) in supine and lateral decubitus postures. In the prone posture V/VA tended to be higher in caudal lung zones.

Effects of unequal pressure swings and different waveforms on distribution of ventilation: a non-linear model simulation

In an attempt to understand the role of unequal pleural pressure swings and of different waveforms of pleural pressure variation in the distribution of ventilation during cyclic breathing, a mathematical model simulation was performed. The computer model which incorporates non-linear resistances and compliances as well as sinusoidal, square, and triangular waveforms of pleural pressure variations indicates that the distribution of ventilation is insensitive to the waveform of the pleural pressure. The distribution is also little changed by the depth of breathing (amplitude), but it is affected significantly by the pattern of different pressures over the regions of the model. For sinusoidal, triangular, and low amplitude square wave pleural pressures with equal amplitudes on both compartments, air was distributed preferentially to the lower compartment under the influence of the static pressure difference. With unequal amplitudes, more air flowed to the compartment experiencing the larger pressure swing. This was virtually independent of the waveform and of the amplitudes of the pleural pressure variation. Comparison of the present results with a constant flow model reveals that the overall distribution of tidal air during cyclic breathing is very different from the results obtained in constant rate inspiration experiments or in bolus distribution experiments. New experiments performed under cyclic breathing conditions are thus indicated.

Flow to lung compartments with different time constants: effect of choice of model

The thesis that an accelerating flow generator provides more even ventilation than a constant flow generator originated from studies using mechanical lung models. We simulated such studies by use of mathematical models. We found that the conclusions of these previous studies were dependent on the particular characteristics of their mechanical models. Studies employing more commonly used models indicate that constant flow generators, in fact, tend to provide more uniform ventilation, especially with long inspiratory times.

A sigmoid model of the static volume-pressure curve of human lung

The authors present a sigmoid mathematical model of the pressure-volume curve of the human lung, based on a relationship between the specific compliance and the maximal pulmonary volume: (see article). This model fits better the experimental data obtained in 20 young normal adults than the currently used exponential model of Salazar and Knowles (1964). The independence between the constant K' and body height is interpreted as a constancy of pulmonary structure for normal subjects of the same age range.