Choking phenomena in a lung-like model

Systems-level airway models of bronchoconstriction

Understanding lung and airway behavior presents a number of challenges, both experimental and theoretical, but the potential rewards are great in terms of both potential treatments for disease and interesting biophysical phenomena. This presents an opportunity for modeling to contribute to greater understanding, and here, we focus on modeling efforts that work toward understanding the behavior of airways in vivo, with an emphasis on asthma. We look particularly at those models that address not just isolated airways but many of the important ways in which airways are coupled both with each other and with other structures. This includes both interesting phenomena involving the airways and the layer of airway smooth muscle that surrounds them, and also the emergence of spatial ventilation patterns via dynamic airway interaction. WIREs Syst Biol Med 2016, 8:459-467. doi: 10.1002/wsbm.1349 For further resources related to this article, please visit the WIREs website.

A global multiscale mathematical model for the human circulation with emphasis on the venous system

We present a global, closed-loop, multiscale mathematical model for the human circulation including the arterial system, the venous system, the heart, the pulmonary circulation and the microcirculation. A distinctive feature of our model is the detailed description of the venous system, particularly for intracranial and extracranial veins. Medium to large vessels are described by one-dimensional hyperbolic systems while the rest of the components are described by zero-dimensional models represented by differential-algebraic equations. Robust, high-order accurate numerical methodology is implemented for solving the hyperbolic equations, which are adopted from a recent reformulation that includes variable material properties. Because of the large intersubject variability of the venous system, we perform a patient-specific characterization of major veins of the head and neck using MRI data. Computational results are carefully validated using published data for the arterial system and most regions of the venous system. For head and neck veins, validation is carried out through a detailed comparison of simulation results against patient-specific phase-contrast MRI flow quantification data. A merit of our model is its global, closed-loop character; the imposition of highly artificial boundary conditions is avoided. Applications in mind include a vast range of medical conditions. Of particular interest is the study of some neurodegenerative diseases, whose venous haemodynamic connection has recently been identified by medical researchers.

Accurate modelling of unsteady flows in collapsible tubes

The context of this paper is the development of a general and efficient numerical haemodynamic tool to help clinicians and researchers in understanding of physiological flow phenomena. We propose an accurate one-dimensional Runge-Kutta discontinuous Galerkin (RK-DG) method coupled with lumped parameter models for the boundary conditions. The suggested model has already been successfully applied to haemodynamics in arteries and is now extended for the flow in collapsible tubes such as veins. The main difference with cardiovascular simulations is that the flow may become supercritical and elastic jumps may appear with the numerical consequence that scheme may not remain monotone if no limiting procedure is introduced. We show that our second-order RK-DG method equipped with an approximate Roe's Riemann solver and a slope-limiting procedure allows us to capture elastic jumps accurately. Moreover, this paper demonstrates that the complex physics associated with such flows is more accurately modelled than with traditional methods such as finite difference methods or finite volumes. We present various benchmark problems that show the flexibility and applicability of the numerical method. Our solutions are compared with analytical solutions when they are available and with solutions obtained using other numerical methods. Finally, to illustrate the clinical interest, we study the emptying process in a calf vein squeezed by contracting skeletal muscle in a normal and pathological subject. We compare our results with experimental simulations and discuss the sensitivity to parameters of our model.

The role of venous valves in pressure shielding

Background

It is widely accepted that venous valves play an important role in reducing the pressure applied to the veins under dynamic load conditions, such as the act of standing up. This understanding is, however, qualitative and not quantitative. The purpose of this paper is to quantify the pressure shielding effect and its variation with a number of system parameters.

Methods

A one-dimensional mathematical model of a collapsible tube, with the facility to introduce valves at any position, was used. The model has been exercised to compute transient pressure and flow distributions along the vein under the action of an imposed gravity field (standing up).

Results

A quantitative evaluation of the effect of a valve, or valves, on the shielding of the vein from peak transient pressure effects was undertaken. The model used reported that a valve decreased the dynamic pressures applied to a vein when gravity is applied by a considerable amount.

Conclusion

The model has the potential to increase understanding of dynamic physical effects in venous physiology, and ultimately might be used as part of an interventional planning tool.

Effect of Repeated Induced Airway Collapse During Total Liquid Ventilation

Negative pressure generated during the expiratory phase of total liquid ventilation (TLV) may induce airway collapse. Evaluation of the effect of repeated airway collapse is crucial to optimize this technique. A total of 24 New Zealand White rabbits were randomly divided into four groups. Ventilation was performed for 6 hours with different strategies: conventional gas ventilation, TLV without airway collapse, and TLV with collapse induced in either 75 or 150 sequential breaths. In the treated groups, airway collapse was induced by increasing the perfluorocarbon drainage velocity while maintaining the minute ventilation constant. Airway pressure, gas exchange, and blood pressure were monitored at 30-minute intervals. At the end of the experiment, airway and lung parenchyma specimens were processed for light microscopy. No evidence of fluorothorax was noticed in any of the four groups at autopsy examination. Minimal signs of inflammation were noticed in all airway and lung parenchyma specimens, but no evident structural alteration was visible. Adequate gas exchange and systemic blood pressure were maintained during all the studies. Repeated airway collapse is not associated with structural changes in the respiratory system and does not alter the gas exchange ability of the lungs.

Expiratory flow limitation during gravitational drainage of perfluorocarbons from liquid-filled lungs

Flow limitation during pressure-driven expiration in liquid-filled lungs was examined in intact, euthanized New Zealand white rabbits. The aim of this study was to further characterize expiratory flow limitation during gravitational drainage of perfluorocarbon liquids from the lungs, and to study the effect of perfluorocarbon type and negative mouth pressure on this phenomenon. Four different perfluorocarbons (PP4, perfluorodecalin, perfluoro-octyl-bromide, and FC-77) were used to examine the effects of density and kinematic viscosity on volume recovered and maximum expiratory flow. It was demonstrated that flow limitation occurs during gravitational drainage when the airway pressure is < or = -15 cm H(2)O, and that this critical value of pressure did not depend on mouth pressure or perfluorocarbon type. The perfluorocarbon properties affect the volume recovered, maximum expiratory flow, and the time to drain, with the most viscous perfluorocarbon (perfluorodecalin) taking the longest time to drain and resulting in lowest maximum expiratory flow. Perfluoro-octyl-bromide resulted in the highest recovered volume. The findings of this study are relevant to the selection of perfluorocarbons to reduce the occurrence of flow limitation and provide adequate minute ventilation during total liquid ventilation.

Location of flow limitation in liquid-filled rabbit lungs

The effects of end-inspiratory lung volume (EILV) and expiratory flow rate (Q) on the location of flow limitation in liquid-filled lungs were investigated by measuring pressure along the airways and by radiographic imaging. The lungs of New Zealand white rabbits were filled with perfluorocarbon to the randomly selected EILV of 20, 30, or 40 ml/kg, and the volume was actively drained at one of three Q: 2.5, 5.0, or 7.5 ml/s. The minimum pressures recorded by a movable catheter at locations along the airways show that flow limitation occurred in the main bronchi and trachea, and was independent of EILV and Q. The minimum pressure at the trachea was -80 mm Hg compared with values that were more positive than -10 mm Hg at a location 3 cm distal to the carina for all EILV and Q combinations. This location was confirmed by the lung images. The airway diameters gradually decreased with time, until flow limitation occurred. In airways distal to the collapse, there was not a significant decrease in diameter. Based on these data, we conclude that flow limitation in liquid-filled lungs occurs in the trachea and main bronchi and its location is independent of EILV or Q.

A Dynamic Morphometric Model of the Normal Lung for Studying Expiratory Flow Limitation in Mechanical Ventilation

A nonlinear dynamic morphometric model of breathing mechanics during artificial ventilation is described. On the basis of the Weibel symmetrical representation of the tracheo-bronchial tree, the model accurately accounts for the geometrical and mechanical characteristics of the conductive zone and packs the respiratory zone into a viscoelastic Voigt body. The model also accounts for the main mechanisms limiting expiratory flow (wave speed limitation and viscous flow limitation), in order to reproduce satisfactorily, under dynamic conditions, the expiratory flow limitation phenomenon occurring in normal subjects when the difference between alveolar pressure and tracheal pressure (driving pressure) is high. Several expirations characterized by different levels of driving pressure are simulated and expiratory flow limitation is detected by plotting the isovolume pressure-flow curves. The model is used to study the time course of resistance and total cross-sectional area as well as the ratio of fluid velocity to wave speed (speed index), in conductive airway generations. The results highlight that the coupling between dissipative pressure losses and airway compliance leads to onset of expiratory flow limitation in normal lungs when driving pressure is increased significantly by applying a subatmospheric pressure to the outlet of the ventilator expiratory channel; wave speed limitation becomes predominant at still higher driving pressures.

Flow Limitation in Liquid-Filled Lungs: Effects of Liquid Properties

Flow limitation in liquid-filled lungs is examined in intact rabbit experiments and a theoretical model. Flow limitation (“choked” flow) occurs when the expiratory flow reaches a maximum value and further increases in driving pressure do not increase the flow. In total liquid ventilation this is characterized by the sudden development of excessively negative airway pressures and airway collapse at the choke point. The occurrence of flow limitation limits the efficacy of total liquid ventilation by reducing the minute ventilation. In this paper we investigate the effects of liquid properties on flow limitation in liquid-filled lungs. It is found that the behavior of liquids with similar densities and viscosities can be quite different. The results of the theoretical model, which incorporates alveolar compliance and airway resistance, agrees qualitatively well with the experimental results. Lung compliance and airway resistance are shown to vary with the perfluorocarbon liquid used to fill the lungs. Surfactant is found to modify the interfacial tension between saline and perfluorocarbon, and surfactant activity at the interface of perfluorocarbon and the native aqueous lining of the lungs appears to induce hysteresis in pressure–volume curves for liquid-filled lungs. Ventilation with a liquid that results in low viscous resistance and high elastic recoil can reduce the amount of liquid remaining in the lungs when choke occurs, and, therefore, may be desirable for liquid ventilation.

A model for time-dependent flow in (giraffe jugular) veins: uniform tube properties

Computations are reported for a one-dimensional model of time-dependent flow in collapsible tubes representing long mammalian veins. The tubes are taken to have uniform intrinsic properties and we concentrate on the effect of longitudinal gravity. The main application is to the jugular vein of the upright giraffe, with given inflow rate from the head, a given pressure, slightly above the external, atmospheric pressure, at the downstream (vena caval) end, and a variety of initial conditions. We show that: (i) previously calculated steady flows are the long time limits of unsteady computations, although only after a considerable time in which slowly-decaying waves and elastic jumps propagate up and down, (ii) steady flows are indeed not found when the steady-flow analysis shown them not to exist, although the consequent unsteadiness is of such small amplitude as to be practically unimportant, (iii) the time taken for the flow to become steady when the neck is raised from the horizontal or the head-down position can be several seconds longer than the neck-raising time itself (3-7s). We also find that roll-waves do not develop despite having been previously predicted for long collapsible tubes. Further application is made to the effect of postural changes on human neck and leg veins.

Interactions of pulsatile upstream forcing with flow-induced oscillations of a collapsed tube: mode-locking

Interest in flow through collapsible tubes derives from their prevalence in the human body. In the circulation at least, the driving pressure for flow is pulsatile, and it is accordingly appropriate to investigate the response of a collapsible tube to a pulsatile head. A servo-controlled hydraulically powered piston pump was used to add pulsation to the head propelling aqueous flow through a silicone rubber tube. The pump was commanded to execute a sinusoidal variation of piston position at various frequencies on either side of the natural frequency of an operating point where slow (3.75 Hz) repetitive self-excited oscillations in the absence of such forcing could be guaranteed. The resulting time series were characterised by the ratio of the number of collapse cycles to the number of forcing cycles in one overall interaction waveform period. Nonlinear interaction rather than linear superposition was dominant. Many different mode-locked interactions were recorded, and are here systematised in Farey series and plots which show the extent of entrainment. A few of the time series were aperiodic over the time scales investigated, suggesting possible chaos.

A nonlinear axisymmetric model with fluid-wall interactions for steady viscous flow in stenotic elastic tubes

Arteries with high-grade stenoses may compress under physiologic conditions due to negative transmural pressure caused by high-velocity flow passing through the stenoses. To quantify the compressive conditions near the stenosis, a nonlinear axisymmetric model with fluid-wall interactions is introduced to simulate the viscous flow in a compliant stenotic tube. The nonlinear elastic properties of the tube (tube law) are measured experimentally and used in the model. The model is solved using ADINA (Automatic Dynamic Incremental Nonlinear Analysis), which is a finite element package capable of solving problems with fluid-structure interactions. Our results indicate that severe stenoses cause critical flow conditions such as negative pressure and high and low shear stresses, which may be related to artery compression, plaque cap rupture, platelet activation, and thrombus formation. The pressure filed near a stenosis has a complex pattern not seen in one-dimensional models. Negative transmural pressure as low as -24 mmHg for a 78 percent stenosis by diameter is observed at the throat of the stenosis for a downstream pressure of 30 mmHg. Maximum shear stress as a high as 1860 dyn/cm2 occurs at the throat of the stenoses, while low shear stress with reversed direction is observed right distal to the stenosis. Compressive stresses are observed inside the tube wall. The maximal principal stress and hoop stress in the 78 percent stenosis are 80 percent higher than that from the 50 percent stenosis used in our simulation. Flow rates under different pressure drop conditions are calculated and compared with experimental measurements and reasonable agreement is found for the prebuckling stage.

A one-dimensional unsteady separable and reattachable flow model for collapsible tube-flow analysis

Taking into account both flow separation and reattachment observed in available experimental results on flows in a quasi-two-dimensional channel, we present a one-dimensional unsteady flow model, which is applicable to a flow in a collapsible tube. The flow model has been derived from the two-dimensional Navier-Stokes equations by introducing the concept of a dividing streamline, which divides a separated flow into a jet and a dead-water zone. We also present a criterion for the determination of a separation point. Numerical results show that the locations of the predicted separation points agree well with the experimental data. The predicted static pressure of the separated flow is almost constant downstream of the separation point and increases quickly just before the reattachment point as observed in the experiment. Finally, using the present flow model and the separation criterion, we examine the oscillatory behavior of an unsteady flow in a symmetric channel whose walls move sinusoidally.

Modeling of airflow in the pharynx with application to sleep apnea

A three-dimensional numerical modeling of airflow in the human pharynx using an anatomically accurate model was conducted. The pharynx walls were assumed to be passive and rigid. The results showed that the pressure drop in the pharynx lies in the range 200-500 Pa. The onset of turbulence was found to increase the pressure drop by 40 percent. A wide range of pharynx geometries covering three sleep apnea treatment therapies (CPAP, mandibular repositioning devices, and surgery) were modeled and the resulting flow characteristics were investigated and compared. The results confirmed that the airflow in the pharynx lies in the laminar-to-turbulence transitional flow regime and thus, a subtle change in the morphology caused by these treatment therapies can significantly affect the airflow characteristics.

Blood pressure and flow rate in the giraffe jugular vein

Experimental measurements in the jugular veins of upright giraffes have shown that the internal pressure is somewhat above atmospheric and increases with height above the heart. A simple model of steady viscous flow in an inverted U-tube shows that these observations are inconsistent with a model in which the blood vessels in the head and neck are effectively rigid and the system resembles a siphon. Instead, the observations indicate that the veins are collapsed and have a high resistance to flow. However, laboratory experiments with collapsible drain tubing in place of the down arm of the U-tube show internal pressure to be exactly atmospheric and uniform with height. A model of viscous flow in a collapsible tube with non-uniform properties is used to suggest that the observed pressure distribution may be a consequence of the intrinsic cross-sectional area and/or compliance of the veins increasing with distance towards the heart, or the external, tissue pressure falling. Finally, the effect of fluid inertia on steady flow in vertical collapsible tubes with uniform intrinsic properties is analysed, and it is shown that a phenomenon of flow limitation is theoretically possible, in which the supercritical flow in the collapsed vein cannot return to the presumably subcritical flow in the open vena cava, even with the help of an 'elastic jump', if the flow rate is too large. The computed critical flow-rate, of about 80 ml s-1, is about twice the flow-rate estimated to be present in the normal giraffe jugular vein. If there were circumstances in which flow limitation occurred in the jugular veins, it would mean that the cerebral blood flow would be limited by downstream conditions, not directly by local requirements.

New model-based indices for maximum expiratory flow-volume curve in patients with chronic obstructive pulmonary disease

New lung function indices based on a lumped parameter model of the maximal expiratory flow-volume (MEFV) curve are presented. The waveforms obtained by the model were compared to the flow-volume curves recorded from normal subjects and from patients with small airways disease, asthma and emphysema. We were able to reproduce the flow-volume curves using the model and calculate new parameters that indicate the degree of lung function impairment and may be applicable to identify mild chronic obstructive pulmonary diseases. Further studies in larger groups of patients are required to better define the true predictive value of the new indices described for the diagnosis of COPD.

Maximum expiratory flow-volume curve: mathematical model and experimental results

A mathematical simulation of the maximum expiratory flow-volume (MEFV) curve was developed using a lumped parameter model. The model uses a theoretical approximation of an activation function representing the lung's pressure-volume relationship during maximally forced expiration. The waveforms obtained by the model were compared to the flow-volume curves recorded from normal subjects and for patients with small airways disease, asthma, and emphysema. We were able to reproduce the flow-volume curves using the model and calculate new parameters that reflect the dependency of airways resistance on expired volume during FVS manoeuvre. These new parameters are based on the entire information presented in the flow-volume curve and on the reduction in flow at all lung volumes. We also calculated the mean slope of the resistance-expired volume curves obtained from the model by fitting a straight line to the curve. Using representative data for normal and COPD patients different mean slopes of 0.095, 0.13, 0.49 and 1.44 litre-1 were obtained for normal subject, small airways disease, asthma and emphysema patients, respectively. The model-based parameters may be applicable to human studies. However, further studies in large groups of patients are required to better define the true predictive value of the new indices described for the diagnosis of COPD.

Numerical schemes for unsteady fluid flow through collapsible tubes

The study of fluid flow through compliant tubes is a fluid-structure type problem, in which a dynamic equilibrium is maintained between the fluid and the tube wall. The analogy between this flow and gas dynamics initiated the use of a number of numerical methods which were originally developed to solve compressible flow in rigid ducts. In this study we investigate the solutions obtained by applying the Lax-Wendroff and MacCormack schemes to one-dimensional incompressible flow through a straight collapsible tube. The time-evolving numerical results were compared with exact steady-state solutions. For boundary conditions which were held fixed after a prescribed rise time, the unsteady numerical solution converges to the exact steady-state solution with very good accuracy. The stability and accuracy of all the methods depend on the amount of viscous pressure loss dictated by wall friction. Flows with undamped oscillations cannot, however, be solved with these techniques.

Effect of stenosis on wall motion. A possible mechanism of stroke and transient ischemic attack

The mechanism by which atherosclerotic plaque causes stroke and transient ischemic attack is not fully understood. One possibility is that the plaque stenosis may set up hemodynamic conditions causing local arterial wall collapse. Arterial wall collapse may, in turn, affect the integrity of the plaque. This study was designed to define the effects of stenosis on the production of arterial wall collapse using a latex tube model. Stenoses ranging up to 81% by diameter were tested in a Starling resistor chamber under pulsatile pressure conditions upstream of the tube. Increasing the degree of stenosis progressively decreased the external pressure necessary to produce collapse, from 37 mm Hg with the 0% stenosis to 24 mm Hg for the 81% stenosis. The stenoses greater than 70% produced a new phenomenon of "systolic wall collapse" just distal to the stenosis. The maximum diameter decrease was 2.83 mm from the baseline diameter of 6.41 mm. Cyclic wall motion just downstream of the stenosis increased with the increased degree of stenosis from 0.34 mm at 0% stenosis to -1.28 mm at 75% stenosis. The phenomena are discussed in terms of simplified Bernoulli pressure drops. We conclude that local arterial stenosis can produce conditions favorable for wall collapse and increased wall motion at physiologic pressure and flow. This collapse may be important in the development of atherosclerotic plaque fracture and subsequent thrombosis or distal embolization.

Simulation of airway closure during forced vital capacity

Airway closure, which disconnects peripheral respiratory units from the trachea, has been observed during expiration to residual volume. It is attributed to dynamic compression that may cause unstable collapse and closure of small airways. During forced vital maneuvers, airway closure is expected to be more significant owing to the maximum expiratory effort. In the present study we have added a simulation of airway closure to the model developed by Elad and associates which simulated flow limitation during forced expiration. Progressive closure is simulated by variation in the number of branches and their cross-sectional areas rather than by change in tube law. The results demonstrate that peripheral airway closure may explain the reduction in maximal flow rate at small lung volumes. It can reproduce either the abrupt fall in maximal expiratory flow-volume curves as observed in dog lungs or the gradual decrease that has been observed in humans.