Convective gas mixing in the airways of the human lung--comparison of laminar and turbulent dispersion

A mathematical model of gas transport in the airways of the human lung with numerical solution of the corresponding differential. equation is presented. The model takes into account, along with the summed cross section of. the Weibel lung model, both convection and longitudinal dispersion of helium and sulphur hexafluoride in air. Simulation was performed using two dispersion coefficients corresponding to laminar and disturbed flow. Moreover, since the dispersion coefficients are closely related to the velocity, five constant flow rates were used for each computation and each simulation. Comparison between the model responses to laminar and turbulent dispersion was made in order to determine which plays the preponderant role in gas transport in the human lung. In addition, agreement between the experimental time constant of CO2 elimination during high-frequency ventilation and the predicted mixing time constant was satisfactory. It is concluded that Taylor laminar dispersion cannot play a significant role in the human airways; however, it seems that convective gas mixing with disturbed dispersion-corresponding to a quasi-steady state?can account for most observed gas transport phenomena during spontaneous breathing and high-frequency ventilation.     

Development of a time-cycled volume-controlled pressure-limited respirator and lung mechanics system for total liquid ventilation

Total liquid ventilation can support gas exchange in animal models of lung injury. Clinical application awaits further technical improvements and performance verification. Our aim was to develop a liquid ventilator, able to deliver accurate tidal volumes, and a computerized system for measuring lung mechanics. The computer-assisted, piston-driven respirator controlled ventilatory parameters that were displayed and modified on a real-time basis. Pressure and temperature transducers along with a lineal displacement controller provided the necessary signals to calculate lung mechanics. Ten newborn lambs (<6 days old) with respiratory failure induced by lung lavage, were monitored using the system. Electromechanical, hydraulic, and data acquisition/analysis components of the ventilator were developed and tested in animals with respiratory failure. All pulmonary signals were collected synchronized in time, displayed in real-time, and archived on digital media. The total mean error (due to transducers, analog-to-digital conversion, amplifiers, etc.) was less than 5% compared with calibrated signals. Components (tubing, pistons, etc.) in contact with exchange fluids were developed so that they could be readily switched, a feature that will be important in clinical settings. Improvements in gas exchange and lung mechanics were observed during liquid ventilation, without impairment of cardiovascular profiles. The total liquid ventilator maintained accurate control of tidal volumes and the sequencing of inspiration/expiration. The computerized system demonstrated its ability to monitor in vivo lung mechanics, providing valuable data for early decision making.     

Optimal application of high-frequency ventilation in infants: atheoretical study

A recent study for preterm infants concluded that high-frequency ventilation (HFV) applied at 15 Hz, in comparison with conventional mechanical ventilation (CMV), did not lead to reduced incidence of barotrauma. The present theoretical study aimed to determine whether computed estimates of lung pressures during HFV and CMV are consistent with these findings. An existing theoretical model of lung mechanics and gas transport in HFV was modified for application to neonates, and new features were incorporated. Simulations were conducted assuming a constant level of eucapnia. It was found that peak alveolar pressures and the magnitude of alveolar pressure swings resulting from HFV at 15 Hz were in general comparable to those produced by CMV in healthy neonates and infants with bronchopulmonary dysplasia. For the latter group, peak alveolar pressures tended to be higher with HFV than in CMV, and application of HFV at 15 Hz was even less advantageous when pulmonary air leak was also present. However, the model predicted that at frequencies between 2 and 4 Hz, alveolar pressure swings and peak alveolar pressures could be minimized, and in some cases, reduced below the levels produced by CMV     

An adaptive lung ventilation controller

Closed loop control of ventilation is traditionally based on end-tidal or mean expired CO₂. The controlled variables are the respiratory rate RR and the tidal volume V_T. Neither patient size or lung mechanics were considered in previous approaches. Also the modes were not suitable for spontaneously breathing subjects. This report presents a new approach to closed loop controlled ventilation, called adaptive lung ventilation (ALV). ALV is based on a pressure controlled ventilation mode suitable for paralyzed, as well as spontaneously breathing, subjects. The clinician enters a desired gross alveolar ventilation (V_gA' in l/min), and the ALV controller tries to achieve this goal by automatic adjustment of mechanical rate and inspiratory pressure level. The adjustments are based on measurements of the patient's lung mechanics and series dead space. The ALV controller was tested on a physical lung model with adjustable mechanical properties. Three different lung pathologies were simulated on the lung model to test the controller for rise time (T₉₀), overshoot (Y_m), and steady state performance (Δ_max ). The pathologies corresponded to restrictive lung disease (similar to ARDS), a “normal” lung, and obstructive lung disease (such as asthma). Furthermore, feasibility tests were done in 6 patients undergoing surgical procedures in total intravenous anesthesia. In the model studies, the controller responded to step changes between 48 seconds and 81 seconds. It did exhibit an overshoot between 5.5% and 7.9% of the setpoint after the step change. The maximal variation of V _gA' in steady-state was between ±4.4% and ±5.6% of the setpoint value after the step change. In the patient study, the controller maintained the set V_gA' and adapted the breathing pattern to the respiratory mechanics of each individual patient     

A Nonlinear Model Combining Pulmonary Mechanics and Gas Concentration Dynamics

To elucidate the various mechanisms by which pulmonary mechanics affect the distribution of gas species throughout the lungs, a multicompartment model relating pressure differences, flows, volumes, and gas species concentrations has been developed. The alveolar regions of the model are nonlinearly elastic and the pressure-flow relation of their associated small airways is volume dependent. Various combinations of parameter values were chosen, including cases in which the model was mechanically uniform (normal) and nonuniform (obstructive). Computer solutions of model equations were obtained for both piecewise-exponential and sinusoidal transpulmonary pressure inputs. Clinical measures of mechanical uniformity and gas concentration homogeneity were evaluated along with unobservable indexes. Results indicate how the distribution of mechanical variables affects the distribution of gas species concentration within the lungs. For the nonuniform (obstructive) model, the gas is distributed more inhomogeneously at higher frequencies and lower lung volumes. The distribution of initial dead space gas to the compartments as well as pendelluft tend to decrease this inhomogeneity. Dynamic compliance for the non-uniform model was frequency dependent at each of the three volume operating points investigated, whereas the semilog nitrogen washout curve was essentially linear for some frequencies and volumes while nonlinear for others. Consequently, inferences about distributions of mechanical parameters and intrapulmonary gas may require that clinical measurements be obtained together at several frequencies and volume operating points.     

Thoracic electrical impedance tomographic measurements during volume controlled ventilation-effects of tidal volume and positive end-expiratory pressure

The aim of the study was to analyze thoracic electrical impedance tomographic (EIT) measurements accomplished under conditions comparable with clinical situations during artificial ventilation. Multiple EIT measurements were performed in pigs in three transverse thoracic planes during the volume controlled mode of mechanical ventilation at various tidal volumes (V(T)) and positive end-expiratory pressures (PEEP). The protocol comprised following ventilatory patterns: 1) V(T)(400, 500, 600, 700 ml) was varied in a random order at various constant PEEP levels and 2) PEEP (2, 5, 8, 11, 14 cm H2O) was randomly modified during ventilation with a constant V(T). The EIT technique was used to generate cross-sectional images of 1) regional lung ventilation and 2) regional shifts in lung volume with PEEP. The quantitative analysis was performed in terms of the tidal amplitude of the impedance change, reflecting the volume of delivered gas at various preset V(T) and the end-expiratory impedance change, revealing the variation of the lung volume at various PEEP levels. The results showed: 1) an increase in the tidal amplitude of the impedance change, proportional to the delivered V(T) at all constant PEEP levels, 2) a rising end-expiratory impedance change, with PEEP reflecting an increase in gas volume, and 3) a PEEP-dependent redistribution of the ventilated gas between the planes. The generated images and the quantitative results indicate the ability of EIT to identify regional changes in V(T) and lung volume during mechanical ventilation.     

Mathematical Modeling of Pulmonary Airway Dynamics

A mathematical model has been derived that describes the pressure-flow relationship in the ventilatory system under conditions of constant lung volume. The parameters of the model include small airway resistance, large airway resistance, and lung elastic recoil. A collapsible airway segment is included to model compression of the airways during expiration.     

Opioid-induced respiratory depression: a mathematical model for fentanyl

In this paper, respiratory depressant effects of fentanyl are described quantitatively by a mathematical model. The model is an extension of a previous one, which reproduces the human ventilatory control system on a physiological basis. It includes the following: three compartments for gas storage and exchange (lungs, body tissue, and brain tissue); the main mechanisms involved in ventilation control (peripheral chemoreceptors, central chemoreceptors, and the central hypoxic depression); and local blood flow regulation. The effects of fentanyl on the respiratory system include a decrease in peripheral and central chemoreceptor gains on ventilation and a direct inhibition of respiratory neural activity. All parameters in the model were chosen according to the literature. The model is able to reproduce the ventilatory effects of fentanyl in several conditions: 1) constant levels of fentanyl; 2) after a bolus injection; 3) at fixed levels of P(ETCO2); and 4) after artificial ventilation. According to the model, in spontaneously breathing subjects, minute ventilation depends on two opposing actions: fentanyl inhibitory influences, which depress ventilation, reducing oxygen tension and increasing CO2 tension, and the consequent activation of chemoreceptors, which stimulates ventilation. Simulations of anesthetized patients resuming spontaneous breathing after artificial ventilation demonstrate the risk of prolonged apnea and tissue hypoxemia. A safe transition can be achieved by increasing patient PCO2 toward the end of artificial ventilation, because an advanced chemoreceptor stimulation is produced, which promptly counteracts fentanyl-induced inhibition at cessation of artificial ventilation.     

A Control System for Long-Term Ventilation of the Lungs

A respirator control system based on a variant process model and optimization of system performance is described. The system attempts to minimize the harmful effects of positive pressure ventilation while meeting the ventilatory requirement of the patient. As alveolar pressure is indicative of respiratory dynamics, it has been used as control parameter. Desired alveolar pressure is derived from a fixed parameter RC lung model while actual alveolar pressure is estimated from the variant lung model which is continuously updated through on-line computation of respiratory mechanical parameters. The controller gain is optimally adjusted so as to minimize error index. The system has been simulated on a digital computer and several representative cases of sudden and gradual parameter variation have been studied. It has been shown that in case of changes in the process, the error quickly damps out to zero.     

A, Model for Tracheobronchial Clearance of Inhaled Particles in Man and a Comparison with Data

We report the development of a mathematical model for the mucociliary clearance of inhaled particles in the normal human lung. The model assumes Weibel's symmetric dichotomously branching system of airways in the lung. The model is formulated by assuming that the particles residing on the surface of the mucus blanket behave as a fluid and that their concentration is governed by the continuity equation. The concentration of particles in each airway generation of the lung is found to depend on the initial deposition pattern and the transport rate of mucus in each airway generation. The distribution of particles is determined by a model calculation which takes into account inertial impaction, gravitational sedimentation, and Brownian diffusion as the principal mechanisms of particle deposition. The mucus transport rates are found by first assuming that the mucus blanket which lines the airways is uniformly thick throughout the entire lung and that there is no net absorption or secretion of mucus in a given airway generation. The only mucociliary transport rate which has been well measured experimentally is in the trachea. We adjust the trachael transport rate in the model until a good agreement between predicted and observed clearance of 7.9?aerodynamic diameter particles from the lung is obtained. The tracheal transport rate necessary to achieve a good fit is 5.5 mm/min which agrees with measured values. With an established trachael transport rate we are then able to calculate transport rates in distal airways.     

Estimating lung mechanics of dogs with unilateral lung injury

Extended least-squares algorithms using transpulmonary pressure and airway flow data from ventilatory waveforms were studied for their ability to track parameters of one- and two-compartment models of lung mechanics. A recursive extended least-squares algorithm with discounted measures estimated parameters of discrete-time models during synchronized intermittent mandatory ventilation. In tests on seven dogs developing oleic acid-induced unilateral hemorrhagic pulmonary edema, the one-compartment estimator responded rapidly and appropriately to changes in mechanics: compliance fell to 0.55 +/- 0.15 of its initial value and resistance rose by a factor of 1.8 +/- 0.5 in 3 h following injection of oleic acid. One-compartment parameter estimates revealed a difference between the airway resistance of inspiration and expiration. Two-compartment estimates were seldom physiologically plausible. The difference between inspiratory and expiratory resistance may have caused the two-compartment estimator to fail when applied to data from the entire respiratory cycle; when only expiratory data were used for estimation, the two-compartment estimates were meaningful. These estimates demonstrated increasing lung inhomogeneity after oleic acid was injected; at the end of 3 h, the ratio of the time constants of the two compartments ranged from 5 to 20 in six of the seven dogs. We conclude that the one- and two-compartment estimates may be combined to provide a meaningful assessment of lung mechanics.     

A computer controller for vest cardiopulmonary resuscitation (CPR)

The authors recently developed a cardiopulmonary resuscitation (CPR) technique in which the airways are obstructed automatically during each chest wall compression. Energy loss accompanying air convection from the lungs during chest wall compression is limited so lung volume and intrathoracic pressures are increased. This technique required the development of a simple controller device to govern the pressure applied to ribcage and abdominal vests together with controller airflow at the airway opening. Experiments with the controller device on eight mongrel dogs showed that cardiac output increased obstructed expiratory cardiopulmonary resuscitation (OECPR) by 19% relative to the cardiac output during standard vest CPR (61% of the prearrest cardiac output relative to 24%, respectively). Furthermore, the OECPR technique without adjunct ventilation resolved the hypocapnic respiratory alkalosis that developed during the standard vest CPR with no ventilatory support. The authors give background information on the obstructed expiratory vest CPR and describe the controller device for delivering this CPR method     

Assessment of closed-loop ventilatory stability in obstructive sleep apnea

Previous studies on ventilatory control in obstructive sleep apnea (OSA) have generally indicated depressed chemosensitivity, implying greater stability of the chemical control of breathing in these subjects. However, these results were based on tests involving steady-state or quasi-steady measurements obtained in wakefulness. We have developed a method for assessing the dynamic stability characteristics of chemoreflex control in OSA patients during sleep. While continuous positive airway pressure was applied to stabilize the upper airways, acoustically stimulated arousals were used to perturb the respiratory system during sleep. The fluctuations in esophageal pressure that ensued were analyzed, using a closed-loop minimal model, to estimate the chemoreflex loop impulse response (CLIR). Tests using simulated data confirmed the validity of our estimation algorithm. Application of the method to arousal responses measured in six OSA and five normal subjects revealed no statistically significant differences in gain margins and loop gain magnitudes between the two groups. However, the CLIR in the OSA subjects exhibited faster and more oscillatory dynamics. This result implies that, in addition to unstable upper airway mechanics, an underdamped chemoreflex control system may be another important factor that promotes the occurrence of periodic obstructive apneas during sleep.     

Mass-Balance Model of Pulmonary Oxygen Transport

A dynamic lumped-parameter model for pulmonary gas transport has been developed to characterize the lung and predict the effect of various parameter changes. The gas side of the lung is modeled as a series and parallel arrangement of five perfectly mixed, variable-volume compartments that correspond roughly to airway and alveolar regions. The blood side of the lung is modeled as a series of perfectly mixed, constant-volume compartments that represent the pulmonary capillary bed. From nonsteady mass balances, equations are derived which yield the time course of concentration for each compartment. Model simulations indicate that the oxygen-hemoglobin reaction does not reach equilibrium in the pulmonary capillaries, an assumption commonly made in analyses of pulmonary oxygen transport. Simulations also show the extent to which breathing amplitude and rate can affect the oxygen level in the blood leaving the lung. A comparison of simulations for a normal state and chronic obstructive lung disease (COLD) with identical input conditions demonstrates that the oxygen level in the blood leaving the lung is much lower in COLD. Also, the simulations are compared with experimental findings.     

Automated Analysis of Intratidal Dynamics of Alveolar Geometry From Microscopic Endoscopy

Alveolar parenchyma, the gas exchange area of the respiratory system, is prone to mechanical damage during mechanical ventilation. Development of lung protective ventilation strategies therefore requires a better understanding of alveolar dynamics during mechanical ventilation. In this paper, we propose a novel method for automated analysis of the intratidal geometry of subpleural alveoli based on the evaluation of video frames recorded from alveolar microscopy in an experimental setting. Our method includes the recording with a microscopic endoscope, feature extraction from image data, the analysis of a single frame, the tracking and analysis of single alveoli in a video sequence, and the evaluation of the obtained sequence of alveolar geometry data. Our method enables automated analysis of 2-D alveolar geometry with sufficient temporal resolution to follow intratidal dynamics. The developed method and the reproducibility of the results were successfully validated with manually segmented video frames.      

On-Line Blood and Respiratory Gas Analysis

Data from a patient receiving ventilatory assistance are processed by computer to calculate pulmonary shunt, dead space/tidal volume ratio, oxygen uptake and delivery, and carbon dioxide elimination and delivery. The computations are based on routines described by Kelman and by Severinghaus, but modified to match limitations of testing imposed by the requirements for ventilatory assistance. Analyses are performed sequentially on arterial and venous blood samples and on respiratory gas samples. The output of the blood gas analyzers is fed on-line to a computer together with other data, such as patient identification, which are manually entered at a keyboard and with thumb-wheel switches. The computer processing begins with determining the concentration of oxygen and carbon dioxide in whole blood and of bicarbonate in plasma. The shunt equation is used to calculate a virtual shunt at therapeutic concentrations of inspired oxygen. Dead space/tidal volume ratios are corrected for mechanical dead space in the respiratory circuit. The analyzed results are returned to the operator within seconds via a video display. Since the data include blood samples from multiple patient sites, a cross-comparison is made by the computer and the operator is informed of unusually large differences in values.     

Measurement of fractional order model parameters of respiratory mechanical impedance in total liquid ventilation

This study presents a methodology for applying the forced-oscillation technique in total liquid ventilation. It mainly consists of applying sinusoidal volumetric excitation to the respiratory system, and determining the transfer function between the delivered flow rate and resulting airway pressure. The investigated frequency range was f ∈ [0.05, 4] Hz at a constant flow amplitude of 7.5 mL/s. The five parameters of a fractional order lung model, the existing "5-parameter constant-phase model," were identified based on measured impedance spectra. The identification method was validated in silico on computer-generated datasets and the overall process was validated in vitro on a simplified single-compartment mechanical lung model. In vivo data on ten newborn lambs suggested the appropriateness of a fractional-order compliance term to the mechanical impedance to describe the low-frequency behavior of the lung, but did not demonstrate the relevance of a fractional-order inertance term. Typical respiratory system frequency response is presented together with statistical data of the measured in vivo impedance model parameters. This information will be useful for both the design of a robust pressure controller for total liquid ventilators and the monitoring of the patient's respiratory parameters during total liquid ventilation treatment.     

An extended soluble gas exchange model for estimating pulmonaryperfusion. I. Derivation and implementation

A dynamic model for respiratory exchange of blood soluble gas is described. This model includes a general treatment of tidal breathing, an inhomogeneous lung comprising multiple distensible compartments, and nonlinearities due to multiple-gas effects. The motivation for this new model is the continuing interest in estimating pulmonary perfusion from measurements of respiratory soluble gas exchange. Numerical simulation can be employed to investigate the errors that result from simplifications made in the derivations of simpler models used for this purpose. Examples of such simplifications are the assumptions that ventilation is constant and unidirectional, and that multiple soluble gases can be independently modeled. These results can delimit the boundaries within which perfusion estimates can be considered reliable. An example demonstrating the model and its numerical solution is presented.     

Limitations of Frequency Dependence as a Measure of Airway Obstruction

The purpose of this study is to develop a pulmonary model and determine the frequency response sensitivity of mechanical parameters such as impedance, dynamic compliance, and dynamic resistance as a function of individual airway properties. Computer simulations of a three compartment model of various physiological cases were used to determine lung parameters as a function of frequency, peripheral airway contribution to total airway resistance, and relative percent obstruction of the peripheral airways. Provided our present concepts of the lung are valid and adequately incorporated into the present model, our results indicate the utility of frequency dependence as a measure of airway obstruction.