Numerical simulation of airflow and microparticle deposition in a synchrotron micro-CT-based pulmonary acinus model

The acinus consists of complex, branched alveolar ducts and numerous surrounding alveoli, and so in this study, we hypothesized that the particle deposition can be much influenced by the complex acinar geometry, and simulated the airflow and particle deposition (density = 1.0 g/cm³, diameter = 1 and 3 μm) numerically in a pulmonary acinar model based on synchrotron micro-CT of the mammalian lung. We assumed that the fluid–structure interaction was neglected and that alveolar flow was induced by the expansion and contraction of the acinar model with the volume changing sinusoidally with time as the moving boundary conditions. The alveolar flow was dominated by radial flows, and a weak recirculating flow was observed at the proximal side of alveoli during the entire respiratory cycle, despite the maximum Reynolds number at the inlet being 0.029. Under zero gravity, the particle deposition rate after single breathing was less than 0.01, although the particles were transported deeply into the acinus after inspiration. Under a gravitational field, the deposition rate and map were influenced strongly by gravity orientation. In the case of a particle diameter of 1 μm, the rate increased dramatically and mostly non-deposited particles remained in the model, indicating that the rate would increase further after repeated breathing. At a particle diameter of 3 μm, the rate was 1.0 and all particles were deposited during single breathing. Our results show that the particle deposition rate in realistic pulmonary acinar model is higher than in an idealized model.     

Regional deposition of particles in the lung during cigarette smoking in humans

Studies were carried out on 11 habitual cigarette smokers to ascertain whether there was a difference in the regional deposition of particles during cigarette smoking compared with tidal breathing and also to investigate whether the ventilatory maneuvers associated with smoking influence the deposition site. A cigarette holder was constructed that permitted cigarette smoke to mix with a radioaerosol. An added resistance simulated the airflow resistance present in a filter-tipped cigarette. Respiratory patterns for the control period of tidal breathing and during smoking were monitored with a respiratory inductance plethysmograph. Smoking resulted in greater apical and central deposition than expected from the distribution of resting ventilation. The changes in the site of deposition during smoking are probably influenced mainly by the properties of the particles concerned, namely, its size, reactivity, and hygroscopicity. Changes in respiratory patterns that occur during inhalation of cigarette smoke may also have an effect but are difficult to quantify and show marked intersubject variation. In selected subjects smoking caused apical deposition to exceed that of the lower zones.     

Effects of oral airway geometry characteristics on the diffusional deposition of inhaled nanoparticles

The deposition of ultrafine aerosols in the respiratory tract presents a significant health risk due to the increased cellular-level response that these particles may invoke. However, the effects of geometric simplifications on local and regional nanoparticle depositions remain unknown for the oral airway and throughout the respiratory tract. The objective of this study is to assess the effects of geometric simplifications on diffusional transport and deposition characteristics of inhaled ultrafine aerosols in models of the extrathoracic oral airway. A realistic model of the oral airway with the nasopharynx (NP) included has been constructed based on computed tomography scans of a healthy adult in conjunction with measurements reported in the literature. Three other geometries with descending degrees of physical realism were then constructed with successive geometric simplifications of the realistic model. A validated low Reynolds number k-omega turbulence model was employed to simulate laminar, transitional, and fully turbulent flow regimes for the transport of 1-200 nm particles. Results of this study indicate that the geometric simplifications considered did not significantly affect the total deposition efficiency or maximum local deposition enhancement of nanoparticles. However, particle transport dynamics and the underlying flow characteristics such as separation, turbulence intensity, and secondary motions did show an observable sensitivity to the geometric complexity. The orientation of the upper trachea was shown to be a major factor determining local deposition downstream of the glottis and should be retained in future models of the respiratory tract. In contrast, retaining the NP produced negligible variations in airway dynamics and could be excluded for predominantly oral breathing conditions. Results of this study corroborate the use of existing diffusion correlations based on a circular oral airway model. In comparison to previous studies, an improved correlation for the deposition of nanoparticles was developed based on a wider range of particle sizes and flow rates, which captures the dependence of the Sherwood number on both Reynolds and Schmidt numbers.     

Models of human lung airways and their application to inhaled particle deposition

Models of the human respiratory tract were developed based on detailed morphometric measurements of a silicone rubber cast of the human tracheobronchial airways. Emphasis was placed on the “Typical Path Lung Model” which used one typical pathway to represent a portion of the lung, such as a lobe, or to represent the whole lung. The models contain geometrical parameters, including airway segment diameters, lengths, branching angles and angles of inclination to gravity, which are needed for estimating inhaled particle deposition. Aerosol depositions for various breathing patterns and particle sizes were calculated using these lung models and the modified Findeisen-Landahl computational scheme. The results agree reasonably well with recent experimental data. Regional deposition, including lobar deposition fractions, are also calculated and compared with results based on the ICRP lung deposition model.     

A Closed-Loop Model of the Respiratory System: Focus on Hypercapnia and Active Expiration

Breathing is a vital process providing the exchange of gases between the lungs and atmosphere. During quiet breathing, pumping air from the lungs is mostly performed by contraction of the diaphragm during inspiration, and muscle contraction during expiration does not play a significant role in ventilation. In contrast, during intense exercise or severe hypercapnia forced or active expiration occurs in which the abdominal “expiratory” muscles become actively involved in breathing. The mechanisms of this transition remain unknown. To study these mechanisms, we developed a computational model of the closed-loop respiratory system that describes the brainstem respiratory network controlling the pulmonary subsystem representing lung biomechanics and gas (O₂ and CO₂) exchange and transport. The lung subsystem provides two types of feedback to the neural subsystem: a mechanical one from pulmonary stretch receptors and a chemical one from central chemoreceptors. The neural component of the model simulates the respiratory network that includes several interacting respiratory neuron types within the Bötzinger and pre-Bötzinger complexes, as well as the retrotrapezoid nucleus/parafacial respiratory group (RTN/pFRG) representing the central chemoreception module targeted by chemical feedback. The RTN/pFRG compartment contains an independent neural generator that is activated at an increased CO₂ level and controls the abdominal motor output. The lung volume is controlled by two pumps, a major one driven by the diaphragm and an additional one activated by abdominal muscles and involved in active expiration. The model represents the first attempt to model the transition from quiet breathing to breathing with active expiration. The model suggests that the closed-loop respiratory control system switches to active expiration via a quantal acceleration of expiratory activity, when increases in breathing rate and phrenic amplitude no longer provide sufficient ventilation. The model can be used for simulation of closed-loop control of breathing under different conditions including respiratory disorders.     

A two-component theory of aerosol deposition in lung airways

The deposition of aerosol particles in the human lung airways is due to two distinct mechanisms. One is by direct deposition resulting from diffusion, sedimentation and impaction as the aerosol moves in and out of the lung. The other is an indirect mechanism by which particles are transported mechanically from the tidal air to the residential air and eventually captured by the airways due to intrinsic particle motion. This last mechanism is not well understood at present. Using a trumpet airway model constructed from Weibel's data, a two-component theory is developed. In this theory, the particle concentrations in the airways and the alveoli at a given airway depth are considered to be quantitatively different. This difference in concentrations will cause a net mixing between the tidal and residential aerosol as the aerosol is breathed in and out. A distribution parameter is then introduced to account for the distribution of ventilation. The effect of intrinsic particle motion on the aerosol mixing is also included. From this theory, total and regional deposition in the lung at the steady mouth breathing without pause is calculated for several different respiratory cycles. The results agree reasonably well with the experimental data.     

Aerosol deposition characteristics in distal acinar airways under cyclic breathing conditions

Although the major mechanisms of aerosol deposition in the lung are known, detailed quantitative data in anatomically realistic models are still lacking, especially in the acinar airways. In this study, an algorithm was developed to build multigenerational three-dimensional models of alveolated airways with arbitrary bifurcation angles and spherical alveolar shape. Using computational fluid dynamics, the deposition of 1- and 3-μm aerosol particles was predicted in models of human alveolar sac and terminal acinar bifurcation under rhythmic wall motion for two breathing conditions (functional residual capacity = 3 liter, tidal volume = 0.5 and 0.9 liter, breathing period = 4 s). Particles entering the model during one inspiration period were tracked for multiple breathing cycles until all particles deposited or escaped from the model. Flow recirculation inside alveoli occurred only during transition between inspiration and expiration and accounted for no more than 1% of the whole cycle. Weak flow irreversibility and convective transport were observed in both models. The average deposition efficiency was similar for both breathing conditions and for both models. Under normal gravity, total deposition was ~33 and 75%, of which ~67 and 96% occurred during the first cycle, for 1- and 3-μm particles, respectively. Under zero gravity, total deposition was ~2-5% for both particle sizes. These results support previous findings that gravitational sedimentation is the dominant deposition mechanism for micrometer-sized aerosols in acinar airways. The results also showed that moving walls and multiple breathing cycles are needed for accurate estimation of aerosol deposition in acinar airways.     

Estimation of respiratory impedance and source pressure using a Thévenin equivalent circuit model

The objective of this paper is to present a new technique which can provide both active respiration source pressure and lung impedance in a single noninvasive test. The method is based upon a Thévenin equivalent circuit model of respiratory mechanics. Using this model, the equivalent source pressure and source impedance can be computed from the measured changes of respiratory pressures and flows in two consecutive cycles before and after addition of purely resistive loads to the mouth. In maximal breathing the source parameters were reproducible in six normal human subjects. The total respiratory resistance during maximal breathing had an average value of 3.46 cmH2O l-1 s-1, and the total dynamic compliance had an average value of 0.078 l cmH2O-1. The airway resistances measured using a plethysmographic method were within the range of 45-65% of the estimated total respiratory resistances. These two resistances were related with a correlation coefficient of 0.98. An average value of the magnitudes of the fundamental components of the source pressure was 6.73 cmH2O during maximal breathing and 2.09 cmH2O during spontaneous breathing.     

Modelling the respiratory airflow pattern by optimization criteria

A model of the control of the respiratory cycle pattern is presented in which the airflow shape is determined by a dynamic optimization problem. The inspiratory and expiratory phases have different performance criteria both of which are related to the oxygen cost of breathing, and to the minimization of tissue damage and control difficulties. The model successfully predicts various patterns of spontaneous breathing during both inspiration and expiration. The effects of applying elastic and resistive loads to the respiratory system can also be predicted. The model performance is in good agreement with the experimental observation that increasing resistance makes the airflow patterns more rectangular.     

Maximization of pulmonary hygroscopic aerosol deposition

A newly developed computer model is used to predict the aqueous salt solution concentration, breathing pattern, and inhaled droplet size distribution parameters that will maximize pulmonary deposition of hygroscopic medicinal aerosols. The parameter values providing maximum pulmonary deposition include 1) a NaCl concentration in the aerosolized solution of 0.035 g/ml or higher if the subject can tolerate it, 2) as nearly a monodispersed inhaled aerosol size distribution as possible, 3) an aerosol mass median diameter of 2-3 micron, and 4) slow (7 breaths/min) uninterrupted breathing of 1.5-2 liters of aerosol/breath. With these values, the model predicts that pulmonary deposition can be increased by greater than 100% relative to the deposition achieved in conventional inhalation therapy with isotonic saline-based medications.     

27. Fuente del Vaquero peat bog (Basque Country,Northern Iberian Peninsula,Spain)

Inhaled particle deposition sites must be identified to effectively treat human airway diseases. We have determined distribution patterns of a selected aeroallergen, ragweed pollen, among human extrathoracic (ET: i.e., oro-nasopharyngeal) regions and the lung. A predictive model validated by inhalation exposure data from human subjects was utilized. Deposition locations were primarily functions of 1. ragweed particle parameters (size: 14–20 μm, shape: spherical, and density: 1.14 g cm^-3) and 2. mode of breathing. In the general population, two styles of inhalation are prevalent: normal augmentors (NAs), and mouth breathers (MBs), their clinical definitions are based on intra-ET airflow divisions. For a NA-mode breathing, sedentary (10 L min^-1) adult, 88% of inhaled ragweed pollen was removed by the ET compartment and 7% collected within the lung. For a MB, the respective deposition efficiencies were 68% and 25%. To apply the model, we used a daily springtime ragweed pollen concentration of 300 grains m^-3 and an exposure time of 0.5 hour to calculate actual doses for the respiratory system. Under the stipulated conditions, a MB would inhale 45 pollen grains per day and 8 would be deposited in the lung; the value is 3 grains for a NA. Frequently, individuals with impaired respiratory functions are MBs in whom such pollen deposits are likely contributors to airway disease.     

Micron-sized intrapulmonary particle deposition in the developing rat lung

Little is known about the effects of postnatal developmental changes in lung architecture and breathing patterns on intrapulmonary particle deposition. We measured deposition in the developing Wistar-Kyoto rat, whose lung development largely parallels that of humans. Deposition of 2-μm sebacate particles was determined in anesthetized, intubated, spontaneously breathing rats on postnatal days (P) 7 to 90 by aerosol photometry (Karrasch S, Eder G, Bolle I, Tsuda A, Schulz H. J Appl Physiol 107: 1293-1299, 2009). Respiratory parameters were determined by body plethysmography. Tidal volume increased substantially from P7 (0.19 ml) to P90 (2.1 ml) while respiratory rate declined from 182 to 107/min. Breath-specific deposition was lowest (9%) at P7 and P90 and markedly higher at P35 (almost 16%). Structural changes of the alveolar region include a ninefold increase in surface area (Bolle I, Eder G, Takenaka S, Ganguly K, Karrasch S, Zeller C, Neuner M, Kreyling WG, Tsuda A, Schulz H. J Appl Physiol 104: 1167-1176, 2008). Particle deposition per unit of time and surface area peaked at P35 and showed a minimum at P90. At an inhaled particle number concentration of 10(5)/cm(3), there was an estimated 450, 690, and 330 particles/(min × cm(2)) at P7, P35, and P90, respectively. Multiple regression models showed that deposition depends on the mean linear intercept as structural component and the breathing parameters, tidal volume, and respiratory rate (r(2) > 0.9). In conclusion, micron-sized particle deposition was dependent on the stage of postnatal lung development. A maximum was observed during late alveolarization (P35), which corresponds to human lungs of about eight years of age. Children at this age may therefore be more susceptible to micron-sized airborne environmental health hazards.     

Self-controlled artificial respiration

We compared respiratory parameters during natural and self-controlled mechanical breathing to investigate mechanisms of respiratory control in alert humans. The self-control of mechanical breathing is realised manually: duration and velocity of air flow are controlled by left and right hands, resp. In this case, the respiratory afferent information is used to control activity of hand muscles but not of breathing muscles. The findings show that lung ventilation during self-controlled mechanical breathing increases by 7.5 l/min. at resting, by 6.3 l/min. during an exercise, as compared with the natural breathing. The increase in the lung ventilation occurs on account of an increase in the tidal volume but the frequency of the self-controlled mechanical breathing tends to be lesser at resting and was statistically significantly lower in exercise that at natural breathing. The exercise increases the lung ventilation by 13.0 l/min. at natural breathing and by 11.8 l/min. during self-controlled mechanical breathing. The findings suggest that the increased lung ventilation during self-controlled mechanical breathing is connected with creation of a new movement skill, and the modified pattern of self-controlled mechanical breathing is caused by a process of cortical transformation of respiratory afferents signals to efferent signals towards the hand muscles.     

The biological age of the respiratory system]

A model of the biological age of the respiratory system is described. The following biological age determinants are used: vital lung capacity, maximal breathing capacity, mid-expiratory flow rate, oxygen consumption. They commonly meet the requirements of the biological age measurement tests as well as reflect main symptoms of the respiratory system ageing. The proposed model has been used to study the peculiarities of the respiratory system ageing in the Abkhasian population and to assess the effect of smoking on this process.     

Stability of the human respiratory control system I. Analysis of a two-dimensional delay state-space model

A number of mathematical models of the human respiratory control system have been developed since 1940 to study a wide range of features of this complex system. Among them, periodic breathing (including Cheyne-Stokes respiration and apneustic breathing) is a collection of regular but involuntary breathing patterns that have important medical implications. The hypothesis that periodic breathing is the result of delay in the feedback signals to the respiratory control system has been studied since the work of Grodins et al. in the early 1950's [12]. The purpose of this paper is to study the stability characteristics of a feedback control system of five differential equations with delays in both the state and control variables presented by Khoo et al. [17] in 1991 for modeling human respiration. The paper is divided in two parts. Part I studies a simplified mathematical model of two nonlinear state equations modeling arterial partial pressures of O2 and CO2 and a peripheral controller. Analysis was done on this model to illuminate the effect of delay on the stability. It shows that delay dependent stability is affected by the controller gain, compartmental volumes and the manner in which changes in the ventilation rate is produced (i.e., by deeper breathing or faster breathing). In addition, numerical simulations were performed to validate analytical results. Part II extends the model in Part I to include both peripheral and central controllers. This, however, necessitates the introduction of a third state equation modeling CO2 levels in the brain. In addition to analytical studies on delay dependent stability, it shows that the decreased cardiac output (and hence increased delay) resulting from the congestive heart condition can induce instability at certain control gain levels. These analytical results were also confirmed by numerical simulations.     

Cyclic model of respiration applied to asymmetrical ventilation and periodic breathing

A model taking into account the cyclic character of respiration in humans is developed using two classical simplifications: CO₂ is the only respiratory gas involved; and respiration is regulated only by a CO₂ linear controller. The model is used to investigate two important clinical aspects of respiratory disease: asymmetrical ventilation and periodic breathing. We show that asymmetry in ventilation significantly influences the time course of the CO₂ partial pressure in the expired alveolar air at the mouth and the elimination of CO₂ through the lungs. Furthermore, the CO₂ controller delay plays a major role in periodic breathing.     

Sample-hold technique for analysis of respiratory gas composition at high breathing frequencies

A gas sampling device is described for continuous monitoring of respiratory gas composition that is applicable to experimental conditions when the breathing frequency is very high (greater than 2 Hz) and the response time of conventional gas analyzers becomes a critical limiting factor. The system utilizes the principle of discontinuous gas collection at any selected point of the respiratory cycle facilitated by ultraspeed piezoelectric valves and includes provision for sample-hold characteristics. Two distinct modes of operation are supported. In phase-locked mode gas sampling is synchronous with breathing frequency. In scanning mode gas collection is asynchronous with breathing frequency. Phase-locked mode may be used for continuous monitoring of end-tidal gas concentrations, whereas scanning mode is intended for assessing the gas concentration profile throughout the respiratory cycle. The system may be applied to steady breathing encountered in mechanical ventilation at high frequency or during quasi-steady breathing observed in panting animals. Combined with a respiratory mass spectrometer, the system has been used for measurement of gas concentrations in alveolar gas mixtures at breathing frequencies ranging from 3 to 30 Hz that were otherwise not amenable to rapid measuring techniques.     

Total respiratory tract deposition of fine micrometer-sized particles in healthy adults: empirical equations for sex and breathing pattern.

Accurate dose estimation under various inhalation conditions is important for assessing both the potential health effects of pollutant particles and the therapeutic efficacy of medicinal aerosols. We measured total deposition fraction (TDF) of monodisperse micrometer-sized particles [particle diameter (Dp) = 1, 3, and 5 microm in diameter] in healthy adults (8 men and 7 women) in a wide range of breathing patterns; tidal volumes (Vt) of 350-1500 ml and respiratory flow rates (Q) of 175-1,000 ml/s. The subject inhaled test aerosols for 10-20 breaths with each of the prescribed breathing patterns, and TDF was obtained by monitoring inhaled and exhaled aerosols breath by breath by a laser aerosol photometer. Results show that TDF varied from 0.12-0.25, 0.26-0.68, and 0.45-0.83 for Dp = 1, 3, and 5 microm, respectively, depending on the breathing pattern used. TDF was comparable between men and women for Dp = 1 microm but was greater in women than men for Dp = 3 and 5 microm for all breathing patterns used (P < 0.05). TDF increased with an increase in Vt regardless of Dp and Q used. At a fixed Vt TDF decreased with an increase in Q for Dp = 1 and 3 microm but did not show any significant changes for Dp = 5 microm. The varying TDF values, however, could be consolidated by a single composite parameter (omega) consisting of Dp, Vt, and Q. The results indicate that unifying empirical formulas provide a convenient means of assessing deposition dose of particles under varying inhalation conditions.     

Disposition of Mulberry Pollen in the Human Respiratory System: A Mathematical Model

Inhaled particle deposition sites must be identified to effectively treat human airway diseases. We have determined distribution patterns of a selected aeroallergen, mulberry pollen, among human extrathoracic (ET: i.e., oronasopharyngeal) regions and the lung. A predictive model validated by inhalation exposure data from human subjects was utilized. Deposition locations were primarily functions of (1) mulberry particle parameters (geometric size, 11–18 μm; shape, spherical; and density, 1.14 g cm^?3), and (2) mode of breathing. In the general population, two styles of inhalation are prevalent, normal augmentors (NAs) and mouth breathers (MBs). Their clinical definitions are based on intra-ET airflow divisions. For a NA-mode breathing sedentary (minute ventilation = V_E = 10 L min^?1) adult, 93% of inhaled mulberry pollen was removed by the ET compartment and 7% collected within the lung. For a MB, the respective deposition efficiencies were 75% and 25%. To apply the model, we used a daily springtime mulberry pollen concentration of 1748 grains m^?3 and an exposure time of 0.5 hour to calculate actual doses for the respiratory system. Under the stipulated conditions, a MB would inhale 524 pollen grains per day and 131 would be deposited in the lung; the value is 37 grains for a NA. Preliminary epidemiological results suggest 15% of the study population are MBs in whom such pollen deposits are likely contributors to airway disease.     

Time-Varying Respiratory System Elastance: A Physiological Model for Patients Who Are Spontaneously Breathing

Background

Respiratory mechanics models can aid in optimising patient-specific mechanical ventilation (MV), but the applications are limited to fully sedated MV patients who have little or no spontaneously breathing efforts. This research presents a time-varying elastance (E_drs) model that can be used in spontaneously breathing patients to determine their respiratory mechanics.

Methods

A time-varying respiratory elastance model is developed with a negative elastic component (E_demand), to describe the driving pressure generated during a patient initiated breathing cycle. Data from 22 patients who are partially mechanically ventilated using Pressure Support (PS) and Neurally Adjusted Ventilatory Assist (NAVA) are used to investigate the physiology relevance of the time-varying elastance model and its clinical potential. E_drs of every breathing cycle for each patient at different ventilation modes are presented for comparison.

Results

At the start of every breathing cycle initiated by patient, E_drs is < 0. This negativity is attributed from the E_demand due to a positive lung volume intake at through negative pressure in the lung compartment. The mapping of E_drs trajectories was able to give unique information to patients’ breathing variability under different ventilation modes. The area under the curve of E_drs (AUCE_drs) for most patients is > 25 cmH₂Os/l and thus can be used as an acute respiratory distress syndrome (ARDS) severity indicator.

Conclusion

The E_drs model captures unique dynamic respiratory mechanics for spontaneously breathing patients with respiratory failure. The model is fully general and is applicable to both fully controlled and partially assisted MV modes.